Page 1 WBJEE - 2011 (Hints & Solutions) Physics & Chemistry 1. A shell of mass m is at rest initially. It explodes into three fragments having masses in the ratio 2 : 2 : 1. the fragments having equal masses fly off along mutually perpendicular direction with speed V. What will be the speed of the third (lighter) fragment? A. From conservation of momentum 1 O2mv 2 mv =+ V 1 = 22v - Hence, velocity of third part is 22v at an angle of 135 o with either part. 2. A small spherical ball of mass m slides without friction from the top of a hemisphere of radius R. A T what height will the ball lose contact with surface of the sphere ? A. If the ball lose contact at B then, from conservation of energy. mg cos? mg sin? R R cos = h ? R - R cos ? N mV 2 R A V () 2 1 mgR 1 cos mv 2 -?= v 2 = 2gR (1 – cos?) ......(i) At B 2 mV N mg cos R += ? When the ball will lose the contact N = O 2 mv mg cos R ?= DESCRIPTIVE TYPE QUESTIONS SUB : PHYSICS & CHEMISTRY Page 2 WBJEE - 2011 (Hints & Solutions) Physics & Chemistry 1. A shell of mass m is at rest initially. It explodes into three fragments having masses in the ratio 2 : 2 : 1. the fragments having equal masses fly off along mutually perpendicular direction with speed V. What will be the speed of the third (lighter) fragment? A. From conservation of momentum 1 O2mv 2 mv =+ V 1 = 22v - Hence, velocity of third part is 22v at an angle of 135 o with either part. 2. A small spherical ball of mass m slides without friction from the top of a hemisphere of radius R. A T what height will the ball lose contact with surface of the sphere ? A. If the ball lose contact at B then, from conservation of energy. mg cos? mg sin? R R cos = h ? R - R cos ? N mV 2 R A V () 2 1 mgR 1 cos mv 2 -?= v 2 = 2gR (1 – cos?) ......(i) At B 2 mV N mg cos R += ? When the ball will lose the contact N = O 2 mv mg cos R ?= DESCRIPTIVE TYPE QUESTIONS SUB : PHYSICS & CHEMISTRY WBJEE - 2011 (Hints & Solutions) Physics & Chemistry V 2 = gR cos ? ........(ii) ? from (i) & (ii) 2Rg(1 - cos ) = gRcos ?? 2 – 2 cos ? = cos ?. 2 = 3 cos ?. ? Height from the ground h = R cos ? = 2R 3 3. Two identical cylindrical vessels, with their bases at the same level, each cotain a liquid of density p. The height of liquid in one vessel in h 1 and that in the other is h 2 . The area of either base is A. What is the work done by gravity in equalizing the levels when the vessles are interconnected ? A. P h 1 A A h 2 ? Let find height = h 12 hh h 2 + ?? ?= ?? ?? decerese in height 12 1 2 1 hh h h hh 22 +- ??? ? ?= - = ??? ? ??? ? Mass of liquid ( ) 12 hh mA 2 - =? ? Work done 12 12 hh hh WA 22 ?- ? - ?? ? ? =? ?? ?? ?? ?? ? ? ?? = () 2 12 hh gA 4 - ? 4. A battery of emf E and internal resistance r is connected across a pure resistive device (such as an electric heater) of resistance R. Prove that the power output of the device will be maximum if R = r. A. I R r E E I Rr = + Page 3 WBJEE - 2011 (Hints & Solutions) Physics & Chemistry 1. A shell of mass m is at rest initially. It explodes into three fragments having masses in the ratio 2 : 2 : 1. the fragments having equal masses fly off along mutually perpendicular direction with speed V. What will be the speed of the third (lighter) fragment? A. From conservation of momentum 1 O2mv 2 mv =+ V 1 = 22v - Hence, velocity of third part is 22v at an angle of 135 o with either part. 2. A small spherical ball of mass m slides without friction from the top of a hemisphere of radius R. A T what height will the ball lose contact with surface of the sphere ? A. If the ball lose contact at B then, from conservation of energy. mg cos? mg sin? R R cos = h ? R - R cos ? N mV 2 R A V () 2 1 mgR 1 cos mv 2 -?= v 2 = 2gR (1 – cos?) ......(i) At B 2 mV N mg cos R += ? When the ball will lose the contact N = O 2 mv mg cos R ?= DESCRIPTIVE TYPE QUESTIONS SUB : PHYSICS & CHEMISTRY WBJEE - 2011 (Hints & Solutions) Physics & Chemistry V 2 = gR cos ? ........(ii) ? from (i) & (ii) 2Rg(1 - cos ) = gRcos ?? 2 – 2 cos ? = cos ?. 2 = 3 cos ?. ? Height from the ground h = R cos ? = 2R 3 3. Two identical cylindrical vessels, with their bases at the same level, each cotain a liquid of density p. The height of liquid in one vessel in h 1 and that in the other is h 2 . The area of either base is A. What is the work done by gravity in equalizing the levels when the vessles are interconnected ? A. P h 1 A A h 2 ? Let find height = h 12 hh h 2 + ?? ?= ?? ?? decerese in height 12 1 2 1 hh h h hh 22 +- ??? ? ?= - = ??? ? ??? ? Mass of liquid ( ) 12 hh mA 2 - =? ? Work done 12 12 hh hh WA 22 ?- ? - ?? ? ? =? ?? ?? ?? ?? ? ? ?? = () 2 12 hh gA 4 - ? 4. A battery of emf E and internal resistance r is connected across a pure resistive device (such as an electric heater) of resistance R. Prove that the power output of the device will be maximum if R = r. A. I R r E E I Rr = + WBJEE - 2011 (Hints & Solutions) Physics & Chemistry Power P = I 2 R = () 2 2 ER Rr + For maximum power dp 0 dR = () () () 2 2 Rr .1 R.2Rr E0 Rr4 ?? +- + = ?? + ?? ?? R + r – 2R = 0 r = R 5. A radioactive isotope X with half life 1.5 × 10 9 yrs. decays into a stable nucleus Y . A rock sample contains both elements X and Y in ratio 1 : 15. Find the age of the rock. A. X Y t = 0, 16 0 t = 1, 1 15 9 1 2 T 1.5 10 yr =× n o 1 NN 2 ?? = ?? ?? 1 = 16 n 1 2 ?? ?? ?? n4 11 n4 22 ?? ? ? =?= ?? ? ? ?? ? ? ? time t = 4 × 1.5 × 10 9 = 6 ×10 9 yrs 6. The bacterial growth follows the rate l aw, dN KN dt = where ‘K’ is a constant and ‘N’ is the number of bacteria cell at any time. If the population of bacteria (no. of cell) is doubled in 5 minutes, find the time by which the population will be eight times of the initial one. A. dN KN dt = (1st order kinetics) ? N = N 0 e kt (integrating) ? in 5 min, N = 2N 0 0 2.303 N Klog tN = Page 4 WBJEE - 2011 (Hints & Solutions) Physics & Chemistry 1. A shell of mass m is at rest initially. It explodes into three fragments having masses in the ratio 2 : 2 : 1. the fragments having equal masses fly off along mutually perpendicular direction with speed V. What will be the speed of the third (lighter) fragment? A. From conservation of momentum 1 O2mv 2 mv =+ V 1 = 22v - Hence, velocity of third part is 22v at an angle of 135 o with either part. 2. A small spherical ball of mass m slides without friction from the top of a hemisphere of radius R. A T what height will the ball lose contact with surface of the sphere ? A. If the ball lose contact at B then, from conservation of energy. mg cos? mg sin? R R cos = h ? R - R cos ? N mV 2 R A V () 2 1 mgR 1 cos mv 2 -?= v 2 = 2gR (1 – cos?) ......(i) At B 2 mV N mg cos R += ? When the ball will lose the contact N = O 2 mv mg cos R ?= DESCRIPTIVE TYPE QUESTIONS SUB : PHYSICS & CHEMISTRY WBJEE - 2011 (Hints & Solutions) Physics & Chemistry V 2 = gR cos ? ........(ii) ? from (i) & (ii) 2Rg(1 - cos ) = gRcos ?? 2 – 2 cos ? = cos ?. 2 = 3 cos ?. ? Height from the ground h = R cos ? = 2R 3 3. Two identical cylindrical vessels, with their bases at the same level, each cotain a liquid of density p. The height of liquid in one vessel in h 1 and that in the other is h 2 . The area of either base is A. What is the work done by gravity in equalizing the levels when the vessles are interconnected ? A. P h 1 A A h 2 ? Let find height = h 12 hh h 2 + ?? ?= ?? ?? decerese in height 12 1 2 1 hh h h hh 22 +- ??? ? ?= - = ??? ? ??? ? Mass of liquid ( ) 12 hh mA 2 - =? ? Work done 12 12 hh hh WA 22 ?- ? - ?? ? ? =? ?? ?? ?? ?? ? ? ?? = () 2 12 hh gA 4 - ? 4. A battery of emf E and internal resistance r is connected across a pure resistive device (such as an electric heater) of resistance R. Prove that the power output of the device will be maximum if R = r. A. I R r E E I Rr = + WBJEE - 2011 (Hints & Solutions) Physics & Chemistry Power P = I 2 R = () 2 2 ER Rr + For maximum power dp 0 dR = () () () 2 2 Rr .1 R.2Rr E0 Rr4 ?? +- + = ?? + ?? ?? R + r – 2R = 0 r = R 5. A radioactive isotope X with half life 1.5 × 10 9 yrs. decays into a stable nucleus Y . A rock sample contains both elements X and Y in ratio 1 : 15. Find the age of the rock. A. X Y t = 0, 16 0 t = 1, 1 15 9 1 2 T 1.5 10 yr =× n o 1 NN 2 ?? = ?? ?? 1 = 16 n 1 2 ?? ?? ?? n4 11 n4 22 ?? ? ? =?= ?? ? ? ?? ? ? ? time t = 4 × 1.5 × 10 9 = 6 ×10 9 yrs 6. The bacterial growth follows the rate l aw, dN KN dt = where ‘K’ is a constant and ‘N’ is the number of bacteria cell at any time. If the population of bacteria (no. of cell) is doubled in 5 minutes, find the time by which the population will be eight times of the initial one. A. dN KN dt = (1st order kinetics) ? N = N 0 e kt (integrating) ? in 5 min, N = 2N 0 0 2.303 N Klog tN = WBJEE - 2011 (Hints & Solutions) Physics & Chemistry ? o 0 2N 2.303 Klog 5N ?? = ?? ?? min –1 ? 2.303 Klog2 5 = for 8N 0 o o 8N 2.303 tlog 2.303 N log 2 5 ?? ?? = ?? ?? ?? ?? ? 53log2 t15min log 2 × == ? time required is 15 min. 7. In ‘x’ ml 0.3 (N) HCl, addition of 200 ml distilled water or addition of 100 ml 0.1 (N) NaOH, gives same final acid strength. Determine ‘x’. A. When 200 ml H 2 O is added to x ml solution (x) (0.3) = (x + 200) (Y) ? final conc. Y = 0.3x 200 x + in 2nd case Number of equivalents of HCl after NaOH addition 0.3x 0.01 1000 - ( no of eq. of NaOH added = 0.01) ? conc. would be 0.3x 0.01 1000 1000(N) 100 x ?? - ?? ?? × + by condition, 0.3x 0.01 1000 0.3x 1000 100 x 200 x ?? - ?? ?? = ++ ? 0.3x 10 0.3x 100 x (200 x) - = ++ ? (0.3x – 10) × (200 + x) = (0.3x)(100 +x) ? 60x – 2000 + 0.3 x 2 – 10x = 30x + 0.3x 2 ? 20x = 2000 ? x = 100 ml 8. Compound A treated with NaNH 2 followed by CH 3 CH 2 Br gave compound B. Partial hydrogenation of compound B produced compound C, which on ozonolysis gave a carbonyl compound D, (C 3 H 6 O). Compound D did not respond to iodoform test with I 2 /Kl and NaOH. Find out the structures of A, B, C and D A. Assuming 1 eq. of NaNH 2 is used, Page 5 WBJEE - 2011 (Hints & Solutions) Physics & Chemistry 1. A shell of mass m is at rest initially. It explodes into three fragments having masses in the ratio 2 : 2 : 1. the fragments having equal masses fly off along mutually perpendicular direction with speed V. What will be the speed of the third (lighter) fragment? A. From conservation of momentum 1 O2mv 2 mv =+ V 1 = 22v - Hence, velocity of third part is 22v at an angle of 135 o with either part. 2. A small spherical ball of mass m slides without friction from the top of a hemisphere of radius R. A T what height will the ball lose contact with surface of the sphere ? A. If the ball lose contact at B then, from conservation of energy. mg cos? mg sin? R R cos = h ? R - R cos ? N mV 2 R A V () 2 1 mgR 1 cos mv 2 -?= v 2 = 2gR (1 – cos?) ......(i) At B 2 mV N mg cos R += ? When the ball will lose the contact N = O 2 mv mg cos R ?= DESCRIPTIVE TYPE QUESTIONS SUB : PHYSICS & CHEMISTRY WBJEE - 2011 (Hints & Solutions) Physics & Chemistry V 2 = gR cos ? ........(ii) ? from (i) & (ii) 2Rg(1 - cos ) = gRcos ?? 2 – 2 cos ? = cos ?. 2 = 3 cos ?. ? Height from the ground h = R cos ? = 2R 3 3. Two identical cylindrical vessels, with their bases at the same level, each cotain a liquid of density p. The height of liquid in one vessel in h 1 and that in the other is h 2 . The area of either base is A. What is the work done by gravity in equalizing the levels when the vessles are interconnected ? A. P h 1 A A h 2 ? Let find height = h 12 hh h 2 + ?? ?= ?? ?? decerese in height 12 1 2 1 hh h h hh 22 +- ??? ? ?= - = ??? ? ??? ? Mass of liquid ( ) 12 hh mA 2 - =? ? Work done 12 12 hh hh WA 22 ?- ? - ?? ? ? =? ?? ?? ?? ?? ? ? ?? = () 2 12 hh gA 4 - ? 4. A battery of emf E and internal resistance r is connected across a pure resistive device (such as an electric heater) of resistance R. Prove that the power output of the device will be maximum if R = r. A. I R r E E I Rr = + WBJEE - 2011 (Hints & Solutions) Physics & Chemistry Power P = I 2 R = () 2 2 ER Rr + For maximum power dp 0 dR = () () () 2 2 Rr .1 R.2Rr E0 Rr4 ?? +- + = ?? + ?? ?? R + r – 2R = 0 r = R 5. A radioactive isotope X with half life 1.5 × 10 9 yrs. decays into a stable nucleus Y . A rock sample contains both elements X and Y in ratio 1 : 15. Find the age of the rock. A. X Y t = 0, 16 0 t = 1, 1 15 9 1 2 T 1.5 10 yr =× n o 1 NN 2 ?? = ?? ?? 1 = 16 n 1 2 ?? ?? ?? n4 11 n4 22 ?? ? ? =?= ?? ? ? ?? ? ? ? time t = 4 × 1.5 × 10 9 = 6 ×10 9 yrs 6. The bacterial growth follows the rate l aw, dN KN dt = where ‘K’ is a constant and ‘N’ is the number of bacteria cell at any time. If the population of bacteria (no. of cell) is doubled in 5 minutes, find the time by which the population will be eight times of the initial one. A. dN KN dt = (1st order kinetics) ? N = N 0 e kt (integrating) ? in 5 min, N = 2N 0 0 2.303 N Klog tN = WBJEE - 2011 (Hints & Solutions) Physics & Chemistry ? o 0 2N 2.303 Klog 5N ?? = ?? ?? min –1 ? 2.303 Klog2 5 = for 8N 0 o o 8N 2.303 tlog 2.303 N log 2 5 ?? ?? = ?? ?? ?? ?? ? 53log2 t15min log 2 × == ? time required is 15 min. 7. In ‘x’ ml 0.3 (N) HCl, addition of 200 ml distilled water or addition of 100 ml 0.1 (N) NaOH, gives same final acid strength. Determine ‘x’. A. When 200 ml H 2 O is added to x ml solution (x) (0.3) = (x + 200) (Y) ? final conc. Y = 0.3x 200 x + in 2nd case Number of equivalents of HCl after NaOH addition 0.3x 0.01 1000 - ( no of eq. of NaOH added = 0.01) ? conc. would be 0.3x 0.01 1000 1000(N) 100 x ?? - ?? ?? × + by condition, 0.3x 0.01 1000 0.3x 1000 100 x 200 x ?? - ?? ?? = ++ ? 0.3x 10 0.3x 100 x (200 x) - = ++ ? (0.3x – 10) × (200 + x) = (0.3x)(100 +x) ? 60x – 2000 + 0.3 x 2 – 10x = 30x + 0.3x 2 ? 20x = 2000 ? x = 100 ml 8. Compound A treated with NaNH 2 followed by CH 3 CH 2 Br gave compound B. Partial hydrogenation of compound B produced compound C, which on ozonolysis gave a carbonyl compound D, (C 3 H 6 O). Compound D did not respond to iodoform test with I 2 /Kl and NaOH. Find out the structures of A, B, C and D A. Assuming 1 eq. of NaNH 2 is used, WBJEE - 2011 (Hints & Solutions) Physics & Chemistry CH CH C CH = 3 2 NaNH 2 – NH 3 CH CH C C Na = 3 2 – + CH CH – Br 3 2 S+ S– S N 2 ? – NaBr CH 3 CH 2 CH = CH CH 2 CH 3 Partial Hydrogenation ????? ? CH 3 CH 2 C = C–CH 2 CH 3 (C) (B) (i) O (ii) Zn + H O 2 3 Ozonolysis 2 CH 3 CH 2 CHO (No Keto Methyl group ? –ve iodoform) (D) 9. An organic compound with molecular formula C 9 H 10 O forms, 2, 4-DNP derivative, reduces Tollen’s reagent and undergoes Cannizzaro reaction. On vigorous oxidation it gives a dicarboxylic acid which is used in the preparation of terylene. Identify the organic compound. A. +ve Brady’s test indicates carbonyl compound, Tollens & Cannizzaro reaction indicates aldehyde without a – H ? end product is terepthalic acid, compound must be CHO CH CH 3 2 [Strong oxidation] COOH COOH (Terepthalic acid) p-ethyl-benzaldehydeRead More

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