Page 1 Time : 3 hrs. M.M. : 360 Answers & Solutions for for for for for JEE (MAIN)2015 Important Instructions : 1. The test is of 3 hours duration. 2. The Test Booklet consists of 90 questions. The maximum marks are 360. 3. There are three parts in the question paper A, B, C consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each question is allotted 4 (four) marks for each correct response. 4. Candidates will be awarded marks as stated above in Instructions No. 3 for correct response of each question. ¼ (onefourth) marks will be deducted for indicating incorrect response of each question. No deduction from the total score will be made if no response is indicated for an item in the answer sheet. 5. There is only one correct response for each question. Filling up more than one response in each question will be treated as wrong response and marks for wrong response will be deducted accordingly as per instruction 4 above. 6. Use Blue/Black Ball Point Pen only for writing particulars/marking responses on Side1 and Side2 of the Answer Sheet. Use of pencil is strictly prohibited. 7. No candidate is allowed to carry any textual material, printed or written, bits of papers, pager, mobile phone, any electronic device, etc. except the Admit Card inside the examination room/hall. 8. The CODE for this Booklet is A. Make sure that the CODE printed on Side2 of the Answer Sheet and also tally the serial number of the Test Booklet and Answer Sheet are the same as that on this booklet. In case of discrepancy, the candidate should immediately report the matter to the Invigilator for replacement of both the Test Booklet and the Answer Sheet. (Physics, Chemistry and Mathematics) Page 2 Time : 3 hrs. M.M. : 360 Answers & Solutions for for for for for JEE (MAIN)2015 Important Instructions : 1. The test is of 3 hours duration. 2. The Test Booklet consists of 90 questions. The maximum marks are 360. 3. There are three parts in the question paper A, B, C consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each question is allotted 4 (four) marks for each correct response. 4. Candidates will be awarded marks as stated above in Instructions No. 3 for correct response of each question. ¼ (onefourth) marks will be deducted for indicating incorrect response of each question. No deduction from the total score will be made if no response is indicated for an item in the answer sheet. 5. There is only one correct response for each question. Filling up more than one response in each question will be treated as wrong response and marks for wrong response will be deducted accordingly as per instruction 4 above. 6. Use Blue/Black Ball Point Pen only for writing particulars/marking responses on Side1 and Side2 of the Answer Sheet. Use of pencil is strictly prohibited. 7. No candidate is allowed to carry any textual material, printed or written, bits of papers, pager, mobile phone, any electronic device, etc. except the Admit Card inside the examination room/hall. 8. The CODE for this Booklet is A. Make sure that the CODE printed on Side2 of the Answer Sheet and also tally the serial number of the Test Booklet and Answer Sheet are the same as that on this booklet. In case of discrepancy, the candidate should immediately report the matter to the Invigilator for replacement of both the Test Booklet and the Answer Sheet. (Physics, Chemistry and Mathematics) JEE (MAIN)2015 2 1. Two stones are thrown up simultaneously from the edge of a cliff 240 m high with initial speed of 10 m/s and 40 m/s respectively. Which of the following graph best represents the time variation of relative position of the second stone with respect to the first? (Assume stones do not rebound after hitting the ground and neglect air resistance, take g = 10 m/s 2 ) (The figures are schematic and not drawn to scale) (1) (y 2 – y 1 ) m 240 8 t (s) 12 t ? (2) (y 2 – y 1 ) m 240 t (s) 12 (3) (y 2 – y 1 ) m 240 8 t (s) 12 (4) (y 2 – y 1 ) m 240 8 t (s) 12 Answer (3) Sol. Till both are in air (From t = 0 to t = 8 sec) ?x = x 2 – x 1 = 30t ??x ? t When second stone hits ground and first stone is in air ?x decreases. PART–A : PHYSICS 2. The period of oscillation of a simple pendulum is 2 L T g ?? . Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch of 1 s resolution. The accuracy in the determination of g is (1) 2% (2) 3% (3) 1% (4) 5% Answer (2) Sol. 2 2 4. l g T ?? ? 100 100 2 100 g lT gl T ? ?? ?? ? ? ? = 100 2. 100 lt lt ?? ?? ? = 0.1 1 100 2 100 20.0 90 ??? ? = 100 200 1 20 3% 200 90 2 9 ?? ? ? 3. A B F Given in the figure are two blocks A and B of weight 20 N and 100 N, respectively. These are being pressed against a wall by a force F as shown. If the coefficient of friction between the blocks is 0.1 and between block B and the wall is 0.15, the frictional force applied by the wall on block B is (1) 100 N (2) 80 N (3) 120 N (4) 150 N Answer (3) Sol. A B 20 N 100 N f s F N Clearly f s = 120 N (for vertical equilibrium of the system) Page 3 Time : 3 hrs. M.M. : 360 Answers & Solutions for for for for for JEE (MAIN)2015 Important Instructions : 1. The test is of 3 hours duration. 2. The Test Booklet consists of 90 questions. The maximum marks are 360. 3. There are three parts in the question paper A, B, C consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each question is allotted 4 (four) marks for each correct response. 4. Candidates will be awarded marks as stated above in Instructions No. 3 for correct response of each question. ¼ (onefourth) marks will be deducted for indicating incorrect response of each question. No deduction from the total score will be made if no response is indicated for an item in the answer sheet. 5. There is only one correct response for each question. Filling up more than one response in each question will be treated as wrong response and marks for wrong response will be deducted accordingly as per instruction 4 above. 6. Use Blue/Black Ball Point Pen only for writing particulars/marking responses on Side1 and Side2 of the Answer Sheet. Use of pencil is strictly prohibited. 7. No candidate is allowed to carry any textual material, printed or written, bits of papers, pager, mobile phone, any electronic device, etc. except the Admit Card inside the examination room/hall. 8. The CODE for this Booklet is A. Make sure that the CODE printed on Side2 of the Answer Sheet and also tally the serial number of the Test Booklet and Answer Sheet are the same as that on this booklet. In case of discrepancy, the candidate should immediately report the matter to the Invigilator for replacement of both the Test Booklet and the Answer Sheet. (Physics, Chemistry and Mathematics) JEE (MAIN)2015 2 1. Two stones are thrown up simultaneously from the edge of a cliff 240 m high with initial speed of 10 m/s and 40 m/s respectively. Which of the following graph best represents the time variation of relative position of the second stone with respect to the first? (Assume stones do not rebound after hitting the ground and neglect air resistance, take g = 10 m/s 2 ) (The figures are schematic and not drawn to scale) (1) (y 2 – y 1 ) m 240 8 t (s) 12 t ? (2) (y 2 – y 1 ) m 240 t (s) 12 (3) (y 2 – y 1 ) m 240 8 t (s) 12 (4) (y 2 – y 1 ) m 240 8 t (s) 12 Answer (3) Sol. Till both are in air (From t = 0 to t = 8 sec) ?x = x 2 – x 1 = 30t ??x ? t When second stone hits ground and first stone is in air ?x decreases. PART–A : PHYSICS 2. The period of oscillation of a simple pendulum is 2 L T g ?? . Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch of 1 s resolution. The accuracy in the determination of g is (1) 2% (2) 3% (3) 1% (4) 5% Answer (2) Sol. 2 2 4. l g T ?? ? 100 100 2 100 g lT gl T ? ?? ?? ? ? ? = 100 2. 100 lt lt ?? ?? ? = 0.1 1 100 2 100 20.0 90 ??? ? = 100 200 1 20 3% 200 90 2 9 ?? ? ? 3. A B F Given in the figure are two blocks A and B of weight 20 N and 100 N, respectively. These are being pressed against a wall by a force F as shown. If the coefficient of friction between the blocks is 0.1 and between block B and the wall is 0.15, the frictional force applied by the wall on block B is (1) 100 N (2) 80 N (3) 120 N (4) 150 N Answer (3) Sol. A B 20 N 100 N f s F N Clearly f s = 120 N (for vertical equilibrium of the system) 3 JEE (MAIN)2015 4. A particle of mass m moving in the x direction with speed 2v is hit by another particle of mass 2m moving in the y direction wth speed v. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to (1) 44% (2) 50% (3) 56% (4) 62% Answer (3) Sol. m 2v 2m v v' ? 22 ' 3 mv v m = KE loss = ?? ?? ? 2 2 11 22 22 mv mv ?? 2 2 122 5 3 23 3 mv mmv m ?? ?? ? ?? ?? ?? Required % = ?? ? 2 22 5 3 100 56% 2 mv mv mv 5. Distance of the centre of mass of a solid uniform cone from its vertex is z 0 . If the radius of its base is R and its height is h then z 0 is equal to (1) 2 4 h R (2) 3 4 h (3) 5 8 h (4) 2 3 8 h R Answer (2) Sol. ?? ? 2 .. dm r dy y R ? h r ???? ?? ?? ? ? ? 2 0 CM 2 1 3 h rdyy ydm y dm Rh ? 3 4 h 6. From a solid sphere of mass M and radius R a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its center and perpendicular to one of its faces is (1) 2 32 2 MR ? (2) 2 16 2 MR ? (3) 2 4 93 MR ? (4) 2 4 33 MR ? Answer (3) Sol. 23 dRa ?? ? 2 3 aR ? 3 3 4 3 3 2 2 3 R M M R ? ??? ? ?? ?? ?? ? 2 ' 3 M M ? ? 2 2 '2 41 636 3 Ma M IR ?? ? ? ? 2 4 93 MR I ? ? 7. From a solid sphere of mass M and radius R, a spherical portion of radius 2 R is removed, as shown in the figure. Taking gravitational potential V = 0 at r = ?, the potential at the centre of the cavity thus formed is (G = gravitational constant) (1) ? 2 GM R (2) ?GM R (3) ?2 3 GM R (4) ?2GM R Page 4 Time : 3 hrs. M.M. : 360 Answers & Solutions for for for for for JEE (MAIN)2015 Important Instructions : 1. The test is of 3 hours duration. 2. The Test Booklet consists of 90 questions. The maximum marks are 360. 3. There are three parts in the question paper A, B, C consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each question is allotted 4 (four) marks for each correct response. 4. Candidates will be awarded marks as stated above in Instructions No. 3 for correct response of each question. ¼ (onefourth) marks will be deducted for indicating incorrect response of each question. No deduction from the total score will be made if no response is indicated for an item in the answer sheet. 5. There is only one correct response for each question. Filling up more than one response in each question will be treated as wrong response and marks for wrong response will be deducted accordingly as per instruction 4 above. 6. Use Blue/Black Ball Point Pen only for writing particulars/marking responses on Side1 and Side2 of the Answer Sheet. Use of pencil is strictly prohibited. 7. No candidate is allowed to carry any textual material, printed or written, bits of papers, pager, mobile phone, any electronic device, etc. except the Admit Card inside the examination room/hall. 8. The CODE for this Booklet is A. Make sure that the CODE printed on Side2 of the Answer Sheet and also tally the serial number of the Test Booklet and Answer Sheet are the same as that on this booklet. In case of discrepancy, the candidate should immediately report the matter to the Invigilator for replacement of both the Test Booklet and the Answer Sheet. (Physics, Chemistry and Mathematics) JEE (MAIN)2015 2 1. Two stones are thrown up simultaneously from the edge of a cliff 240 m high with initial speed of 10 m/s and 40 m/s respectively. Which of the following graph best represents the time variation of relative position of the second stone with respect to the first? (Assume stones do not rebound after hitting the ground and neglect air resistance, take g = 10 m/s 2 ) (The figures are schematic and not drawn to scale) (1) (y 2 – y 1 ) m 240 8 t (s) 12 t ? (2) (y 2 – y 1 ) m 240 t (s) 12 (3) (y 2 – y 1 ) m 240 8 t (s) 12 (4) (y 2 – y 1 ) m 240 8 t (s) 12 Answer (3) Sol. Till both are in air (From t = 0 to t = 8 sec) ?x = x 2 – x 1 = 30t ??x ? t When second stone hits ground and first stone is in air ?x decreases. PART–A : PHYSICS 2. The period of oscillation of a simple pendulum is 2 L T g ?? . Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch of 1 s resolution. The accuracy in the determination of g is (1) 2% (2) 3% (3) 1% (4) 5% Answer (2) Sol. 2 2 4. l g T ?? ? 100 100 2 100 g lT gl T ? ?? ?? ? ? ? = 100 2. 100 lt lt ?? ?? ? = 0.1 1 100 2 100 20.0 90 ??? ? = 100 200 1 20 3% 200 90 2 9 ?? ? ? 3. A B F Given in the figure are two blocks A and B of weight 20 N and 100 N, respectively. These are being pressed against a wall by a force F as shown. If the coefficient of friction between the blocks is 0.1 and between block B and the wall is 0.15, the frictional force applied by the wall on block B is (1) 100 N (2) 80 N (3) 120 N (4) 150 N Answer (3) Sol. A B 20 N 100 N f s F N Clearly f s = 120 N (for vertical equilibrium of the system) 3 JEE (MAIN)2015 4. A particle of mass m moving in the x direction with speed 2v is hit by another particle of mass 2m moving in the y direction wth speed v. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to (1) 44% (2) 50% (3) 56% (4) 62% Answer (3) Sol. m 2v 2m v v' ? 22 ' 3 mv v m = KE loss = ?? ?? ? 2 2 11 22 22 mv mv ?? 2 2 122 5 3 23 3 mv mmv m ?? ?? ? ?? ?? ?? Required % = ?? ? 2 22 5 3 100 56% 2 mv mv mv 5. Distance of the centre of mass of a solid uniform cone from its vertex is z 0 . If the radius of its base is R and its height is h then z 0 is equal to (1) 2 4 h R (2) 3 4 h (3) 5 8 h (4) 2 3 8 h R Answer (2) Sol. ?? ? 2 .. dm r dy y R ? h r ???? ?? ?? ? ? ? 2 0 CM 2 1 3 h rdyy ydm y dm Rh ? 3 4 h 6. From a solid sphere of mass M and radius R a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its center and perpendicular to one of its faces is (1) 2 32 2 MR ? (2) 2 16 2 MR ? (3) 2 4 93 MR ? (4) 2 4 33 MR ? Answer (3) Sol. 23 dRa ?? ? 2 3 aR ? 3 3 4 3 3 2 2 3 R M M R ? ??? ? ?? ?? ?? ? 2 ' 3 M M ? ? 2 2 '2 41 636 3 Ma M IR ?? ? ? ? 2 4 93 MR I ? ? 7. From a solid sphere of mass M and radius R, a spherical portion of radius 2 R is removed, as shown in the figure. Taking gravitational potential V = 0 at r = ?, the potential at the centre of the cavity thus formed is (G = gravitational constant) (1) ? 2 GM R (2) ?GM R (3) ?2 3 GM R (4) ?2GM R JEE (MAIN)2015 4 Answer (2) Sol. V = V 1 – V 2 2 2 1 3 3 2 2 GM R V R R ?? ?? ?? ? ?? ?? ?? ?? 2 3 8 2 2 M G V R ?? ?? ?? ?? ?? ?? ?? ? GM V R ? ? 8. A pendulum made of a uniform wire of cross sectional area A has time period T. When an additional mass M is added to its bob, the time period changes to T M . If the Young's modulus of the material of the wire is Y then 1 Y is equal to (g = gravitational acceleration) (1) ?? ?? ? ?? ?? ?? ?? ?? 2 1 M T A TMg (2) ?? ?? ? ?? ?? ?? ?? ?? 2 1 M Mg T TA (3) ?? ?? ??? ?? ?? ?? ?? 2 1 M T A TMg (4) ?? ?? ?? ? ?? ?? ?? ?? 2 1 M TA TMg Answer (1) Sol. ?? 2 l T g ...(1) ?? ?? 2 M ll T g ...(2) ? ??? ? Mgl Fl Yl AlAY ...(3) ?? ?? ??? ?? ?? ?? ?? ?? 2 1 1 M T A YMg T 9. Consider a spherical shell of radius R at temperature T. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume 4 U uT V ?? and pressure ?? ? ?? ?? 1 3 U P V . If the shell now undergoes an adiabatic expansion the relation between T and R is (1) T ? e –R (2) T ? e –3R (3) 1 T R ? (4) 3 1 T R ? Answer (3) Sol. 4 11 33 U PkT V ?? ?? ?? ?? ...(i) PV = ?RT ...(ii) 4 1 3 RT kT V ? ? ? V ? T –3 1 R T ? 10. A solid body of constant heat capacity 1 J/°C is being heated by keeping it in contact with reservoirs in two ways : (i) Sequentially keeping in contact with 2 reservoirs such that each reservoir supplies same amount of heat. (ii) Sequentially keeping in contact with 8 reservoirs such that each reservoir supplies same amount of heat. In both the cases body is brought from initial temperature 100°C to final temperature 200°C. Entropy change of the body in the two cases respectively is (1) ln 2, 4ln 2 (2) ln 2, ln 2 (3) ln 2, 2ln 2 (4) 2ln 2, 8ln 2 Answer (None) Sol. dQ dT ds ms TT ??? ?? ?? ? ? ? ?? 2 1 473 1log log 373 ee T dT sds ms TT 11. Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as V q , where V is the volume of the gas. The value of q is ?? ?? ?? ?? P v C C (1) ? ? 35 6 (2) ? ? 35 6 (3) ? ?1 2 (4) ? ?1 2 Answer (3) Sol. ? ?? ? ?? ? ?? ?? rms 2 1 3 2 v RT N d M V ...(i) V T ?? ...(ii) Page 5 Time : 3 hrs. M.M. : 360 Answers & Solutions for for for for for JEE (MAIN)2015 Important Instructions : 1. The test is of 3 hours duration. 2. The Test Booklet consists of 90 questions. The maximum marks are 360. 3. There are three parts in the question paper A, B, C consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each question is allotted 4 (four) marks for each correct response. 4. Candidates will be awarded marks as stated above in Instructions No. 3 for correct response of each question. ¼ (onefourth) marks will be deducted for indicating incorrect response of each question. No deduction from the total score will be made if no response is indicated for an item in the answer sheet. 5. There is only one correct response for each question. Filling up more than one response in each question will be treated as wrong response and marks for wrong response will be deducted accordingly as per instruction 4 above. 6. Use Blue/Black Ball Point Pen only for writing particulars/marking responses on Side1 and Side2 of the Answer Sheet. Use of pencil is strictly prohibited. 7. No candidate is allowed to carry any textual material, printed or written, bits of papers, pager, mobile phone, any electronic device, etc. except the Admit Card inside the examination room/hall. 8. The CODE for this Booklet is A. Make sure that the CODE printed on Side2 of the Answer Sheet and also tally the serial number of the Test Booklet and Answer Sheet are the same as that on this booklet. In case of discrepancy, the candidate should immediately report the matter to the Invigilator for replacement of both the Test Booklet and the Answer Sheet. (Physics, Chemistry and Mathematics) JEE (MAIN)2015 2 1. Two stones are thrown up simultaneously from the edge of a cliff 240 m high with initial speed of 10 m/s and 40 m/s respectively. Which of the following graph best represents the time variation of relative position of the second stone with respect to the first? (Assume stones do not rebound after hitting the ground and neglect air resistance, take g = 10 m/s 2 ) (The figures are schematic and not drawn to scale) (1) (y 2 – y 1 ) m 240 8 t (s) 12 t ? (2) (y 2 – y 1 ) m 240 t (s) 12 (3) (y 2 – y 1 ) m 240 8 t (s) 12 (4) (y 2 – y 1 ) m 240 8 t (s) 12 Answer (3) Sol. Till both are in air (From t = 0 to t = 8 sec) ?x = x 2 – x 1 = 30t ??x ? t When second stone hits ground and first stone is in air ?x decreases. PART–A : PHYSICS 2. The period of oscillation of a simple pendulum is 2 L T g ?? . Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch of 1 s resolution. The accuracy in the determination of g is (1) 2% (2) 3% (3) 1% (4) 5% Answer (2) Sol. 2 2 4. l g T ?? ? 100 100 2 100 g lT gl T ? ?? ?? ? ? ? = 100 2. 100 lt lt ?? ?? ? = 0.1 1 100 2 100 20.0 90 ??? ? = 100 200 1 20 3% 200 90 2 9 ?? ? ? 3. A B F Given in the figure are two blocks A and B of weight 20 N and 100 N, respectively. These are being pressed against a wall by a force F as shown. If the coefficient of friction between the blocks is 0.1 and between block B and the wall is 0.15, the frictional force applied by the wall on block B is (1) 100 N (2) 80 N (3) 120 N (4) 150 N Answer (3) Sol. A B 20 N 100 N f s F N Clearly f s = 120 N (for vertical equilibrium of the system) 3 JEE (MAIN)2015 4. A particle of mass m moving in the x direction with speed 2v is hit by another particle of mass 2m moving in the y direction wth speed v. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to (1) 44% (2) 50% (3) 56% (4) 62% Answer (3) Sol. m 2v 2m v v' ? 22 ' 3 mv v m = KE loss = ?? ?? ? 2 2 11 22 22 mv mv ?? 2 2 122 5 3 23 3 mv mmv m ?? ?? ? ?? ?? ?? Required % = ?? ? 2 22 5 3 100 56% 2 mv mv mv 5. Distance of the centre of mass of a solid uniform cone from its vertex is z 0 . If the radius of its base is R and its height is h then z 0 is equal to (1) 2 4 h R (2) 3 4 h (3) 5 8 h (4) 2 3 8 h R Answer (2) Sol. ?? ? 2 .. dm r dy y R ? h r ???? ?? ?? ? ? ? 2 0 CM 2 1 3 h rdyy ydm y dm Rh ? 3 4 h 6. From a solid sphere of mass M and radius R a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its center and perpendicular to one of its faces is (1) 2 32 2 MR ? (2) 2 16 2 MR ? (3) 2 4 93 MR ? (4) 2 4 33 MR ? Answer (3) Sol. 23 dRa ?? ? 2 3 aR ? 3 3 4 3 3 2 2 3 R M M R ? ??? ? ?? ?? ?? ? 2 ' 3 M M ? ? 2 2 '2 41 636 3 Ma M IR ?? ? ? ? 2 4 93 MR I ? ? 7. From a solid sphere of mass M and radius R, a spherical portion of radius 2 R is removed, as shown in the figure. Taking gravitational potential V = 0 at r = ?, the potential at the centre of the cavity thus formed is (G = gravitational constant) (1) ? 2 GM R (2) ?GM R (3) ?2 3 GM R (4) ?2GM R JEE (MAIN)2015 4 Answer (2) Sol. V = V 1 – V 2 2 2 1 3 3 2 2 GM R V R R ?? ?? ?? ? ?? ?? ?? ?? 2 3 8 2 2 M G V R ?? ?? ?? ?? ?? ?? ?? ? GM V R ? ? 8. A pendulum made of a uniform wire of cross sectional area A has time period T. When an additional mass M is added to its bob, the time period changes to T M . If the Young's modulus of the material of the wire is Y then 1 Y is equal to (g = gravitational acceleration) (1) ?? ?? ? ?? ?? ?? ?? ?? 2 1 M T A TMg (2) ?? ?? ? ?? ?? ?? ?? ?? 2 1 M Mg T TA (3) ?? ?? ??? ?? ?? ?? ?? 2 1 M T A TMg (4) ?? ?? ?? ? ?? ?? ?? ?? 2 1 M TA TMg Answer (1) Sol. ?? 2 l T g ...(1) ?? ?? 2 M ll T g ...(2) ? ??? ? Mgl Fl Yl AlAY ...(3) ?? ?? ??? ?? ?? ?? ?? ?? 2 1 1 M T A YMg T 9. Consider a spherical shell of radius R at temperature T. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume 4 U uT V ?? and pressure ?? ? ?? ?? 1 3 U P V . If the shell now undergoes an adiabatic expansion the relation between T and R is (1) T ? e –R (2) T ? e –3R (3) 1 T R ? (4) 3 1 T R ? Answer (3) Sol. 4 11 33 U PkT V ?? ?? ?? ?? ...(i) PV = ?RT ...(ii) 4 1 3 RT kT V ? ? ? V ? T –3 1 R T ? 10. A solid body of constant heat capacity 1 J/°C is being heated by keeping it in contact with reservoirs in two ways : (i) Sequentially keeping in contact with 2 reservoirs such that each reservoir supplies same amount of heat. (ii) Sequentially keeping in contact with 8 reservoirs such that each reservoir supplies same amount of heat. In both the cases body is brought from initial temperature 100°C to final temperature 200°C. Entropy change of the body in the two cases respectively is (1) ln 2, 4ln 2 (2) ln 2, ln 2 (3) ln 2, 2ln 2 (4) 2ln 2, 8ln 2 Answer (None) Sol. dQ dT ds ms TT ??? ?? ?? ? ? ? ?? 2 1 473 1log log 373 ee T dT sds ms TT 11. Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as V q , where V is the volume of the gas. The value of q is ?? ?? ?? ?? P v C C (1) ? ? 35 6 (2) ? ? 35 6 (3) ? ?1 2 (4) ? ?1 2 Answer (3) Sol. ? ?? ? ?? ? ?? ?? rms 2 1 3 2 v RT N d M V ...(i) V T ?? ...(ii) 5 JEE (MAIN)2015 TV ? – 1 = k ...(iii) ? ? ? ?? 1 2 V 12. For a simple pendulum, a graph is plotted between its kinetic energy (KE) and potential energy (PE) against its displacement d. Which one of the following represents these correctly? (Graphs are schematic and not drawn to scale) (1) E KE d PE (2) E KE d PE (3) E KE d PE (4) E PE KE Answer (2) Sol. ?? ? 22 2 1 KE ( ) 2 mA d ?? 22 1 PE 2 md At d = ± A, PE = maximum while KE = 0. 13. A train is moving on a straight track with speed 20 ms –1 . It is blowing its whistle at the frequency of 1000 Hz. The percentage change in the frequency heard by a person standing near the track as the train passes him is (speed of sound = 320 ms –1 ) close to (1) 6% (2) 12% (3) 18% (4) 24% Answer (2) Sol. ?? ?? ?? ?? ?? ?? ?? ?? ?? 1 320 320 Hz 320 20 300 s v ff f f vv ?? ??? ?? ? ?? 2 320 Hz 340 s v ff f vv ??? ? ? ?? ? ? ??? ? ??? ? 221 11 100 1 100 fff ff ?? ??? ?? ?? 300 100 1 12% 340 14. A long cylindrical shell carries positive surface charge ? in the upper half and negative surface charge – ? in the lower half. The electric field lines around the cylinder will look like figure given in (figures are schematic and not drawn to scale) (1) + + ++ + + – – – – – – – – (2) + + + + + + – – – – – – – – (3) + + ++ + + – – – – – – – – (4) Answer (1) Sol. The field line should resemble that of a dipole. 15. A uniformly charged solid sphere of radius R has potential V 0 (measured with respect to ?) on its surface. For this sphere the equipotential surfaces with potentials 000 0 353 ,, and 24 4 4 VVV V have radius R 1 , R 2 , R 3 and R 4 respectively. Then (1) R 1 = 0 and R 2 > (R 4 – R 3 ) (2) R 1 ? 0 and (R 2 – R 1 ) > (R 4 – R 3 ) (3) R 1 = 0 and R 2 < (R 4 – R 3 ) (4) 2R < R 4Read More
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