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Page 1 4.1 SOLUTIONS TO CONCEPTS CHAPTER – 4 1. m = 1 gm = 1/1000 kg F = 6.67 × 10 –17 N ? F = 2 2 1 r m Gm ? 6.67 × 20 –17 = 2 11 r ) 1000 / 1 ( ) 1000 / 1 ( 10 67 . 6 ? ? ? ? ? r 2 = 17 17 17 6 11 10 10 10 64 . 6 10 10 67 . 6 ? ? ? ? ? ? ? ? ? = 1 ? r = 1 = 1 metre. So, the separation between the particles is 1 m. 2. A man is standing on the surface of earth The force acting on the man = mg ………(i) Assuming that, m = mass of the man = 50 kg And g = acceleration due to gravity on the surface of earth = 10 m/s 2 W = mg = 50× 10= 500 N = force acting on the man So, the man is also attracting the earth with a force of 500 N 3. The force of attraction between the two charges = 2 9 2 2 1 o r 1 10 9 r q q 4 1 ? ? ?? The force of attraction is equal to the weight Mg = 2 9 r 10 9 ? ? r 2 = m 10 9 10 m 10 9 8 9 ? ? ? ? [Taking g=10 m/s 2 ] ? r = m 10 3 m 10 9 4 8 ? ? ? mt For example, Assuming m= 64 kg, r = 4 4 10 8 3 64 10 3 ? ? = 3750 m 4. mass = 50 kg r = 20 cm = 0.2 m 04 . 0 2500 10 67 . 6 r m m G F 11 2 2 1 G ? ? ? ? ? Coulomb’s force F C = 2 2 1 o r q q 4 1 ?? = 9 × 10 9 04 . 0 q 2 Since, F G = F c = 04 . 0 q 10 9 04 . 0 2500 10 7 . 6 2 9 11 ? ? ? ? ? ? ? q 2 = 25 10 9 10 7 . 6 04 . 0 2500 10 7 . 6 9 9 11 ? ? ? ? ? ? ? ? = 18.07 × 10 –18 q = -18 10 18.07 ? = 4.3 × 10 -9 C. m 1 = 1 gm m 2 = 1 gm r Page 2 4.1 SOLUTIONS TO CONCEPTS CHAPTER – 4 1. m = 1 gm = 1/1000 kg F = 6.67 × 10 –17 N ? F = 2 2 1 r m Gm ? 6.67 × 20 –17 = 2 11 r ) 1000 / 1 ( ) 1000 / 1 ( 10 67 . 6 ? ? ? ? ? r 2 = 17 17 17 6 11 10 10 10 64 . 6 10 10 67 . 6 ? ? ? ? ? ? ? ? ? = 1 ? r = 1 = 1 metre. So, the separation between the particles is 1 m. 2. A man is standing on the surface of earth The force acting on the man = mg ………(i) Assuming that, m = mass of the man = 50 kg And g = acceleration due to gravity on the surface of earth = 10 m/s 2 W = mg = 50× 10= 500 N = force acting on the man So, the man is also attracting the earth with a force of 500 N 3. The force of attraction between the two charges = 2 9 2 2 1 o r 1 10 9 r q q 4 1 ? ? ?? The force of attraction is equal to the weight Mg = 2 9 r 10 9 ? ? r 2 = m 10 9 10 m 10 9 8 9 ? ? ? ? [Taking g=10 m/s 2 ] ? r = m 10 3 m 10 9 4 8 ? ? ? mt For example, Assuming m= 64 kg, r = 4 4 10 8 3 64 10 3 ? ? = 3750 m 4. mass = 50 kg r = 20 cm = 0.2 m 04 . 0 2500 10 67 . 6 r m m G F 11 2 2 1 G ? ? ? ? ? Coulomb’s force F C = 2 2 1 o r q q 4 1 ?? = 9 × 10 9 04 . 0 q 2 Since, F G = F c = 04 . 0 q 10 9 04 . 0 2500 10 7 . 6 2 9 11 ? ? ? ? ? ? ? q 2 = 25 10 9 10 7 . 6 04 . 0 2500 10 7 . 6 9 9 11 ? ? ? ? ? ? ? ? = 18.07 × 10 –18 q = -18 10 18.07 ? = 4.3 × 10 -9 C. m 1 = 1 gm m 2 = 1 gm r Chapter-4 4.2 5. The limb exerts a normal force 48 N and frictional force of 20 N. Resultant magnitude of the force, R = 2 2 ) 20 ( ) 48 ( ? = 400 2304 ? = 2704 = 52 N 6. The body builder exerts a force = 150 N. Compression x = 20 cm = 0.2 m ?Total force exerted by the man = f = kx ? kx = 150 ? k = 2 . 0 150 = 2 1500 = 750 N/m 7. Suppose the height is h. At earth station F = GMm/R 2 M = mass of earth m = mass of satellite R = Radius of earth F= 2 ) h R ( GMm ? = 2 R 2 GMm ? 2R 2 = (R + h) 2 ? R 2 – h 2 – 2Rh = 0 ? h 2 + 2Rh – R 2 = 0 H = 2 R 4 R 4 R 2 2 2 ? ? ? ? ? ? ? ? ? = 2 R 2 2 R 2 ? ? = –R ± R 2 = R ? ? 1 2 ? = 6400 × (0.414) = 2649.6 = 2650 km 8. Two charged particle placed at a sehortion 2m. exert a force of 20m. F 1 = 20 N. r 1 = 20 cm F 2 = ? r 2 = 25 cm Since, F = 2 2 1 o r q q 4 1 ?? , F ? 2 r 1 2 1 2 2 2 1 r r F F ? ? F 2 = F 1 × 2 2 1 r r ? ? ? ? ? ? ? ? = 20 × 2 25 20 ? ? ? ? ? ? = 20 × 25 16 = 5 64 = 12.8 N = 13 N. 9. The force between the earth and the moon, F= G 2 c m r m m F = ? ? 2 8 24 22 11 10 8 . 3 10 6 10 36 . 7 10 67 . 6 ? ? ? ? ? ? ? = ? ? 16 2 35 10 8 . 3 10 36 . 7 67 . 6 ? ? ? = 20.3 × 10 19 =2.03 × 10 20 N = 2 ×10 20 N 10. Charge on proton = 1.6 × 10 –19 ? F electrical = 2 2 1 o r q q 4 1 ? ?? = ? ? 2 38 2 9 r 10 6 . 1 10 9 ? ? ? ? mass of proton = 1.732 × 10 –27 kg 48N x F F Page 3 4.1 SOLUTIONS TO CONCEPTS CHAPTER – 4 1. m = 1 gm = 1/1000 kg F = 6.67 × 10 –17 N ? F = 2 2 1 r m Gm ? 6.67 × 20 –17 = 2 11 r ) 1000 / 1 ( ) 1000 / 1 ( 10 67 . 6 ? ? ? ? ? r 2 = 17 17 17 6 11 10 10 10 64 . 6 10 10 67 . 6 ? ? ? ? ? ? ? ? ? = 1 ? r = 1 = 1 metre. So, the separation between the particles is 1 m. 2. A man is standing on the surface of earth The force acting on the man = mg ………(i) Assuming that, m = mass of the man = 50 kg And g = acceleration due to gravity on the surface of earth = 10 m/s 2 W = mg = 50× 10= 500 N = force acting on the man So, the man is also attracting the earth with a force of 500 N 3. The force of attraction between the two charges = 2 9 2 2 1 o r 1 10 9 r q q 4 1 ? ? ?? The force of attraction is equal to the weight Mg = 2 9 r 10 9 ? ? r 2 = m 10 9 10 m 10 9 8 9 ? ? ? ? [Taking g=10 m/s 2 ] ? r = m 10 3 m 10 9 4 8 ? ? ? mt For example, Assuming m= 64 kg, r = 4 4 10 8 3 64 10 3 ? ? = 3750 m 4. mass = 50 kg r = 20 cm = 0.2 m 04 . 0 2500 10 67 . 6 r m m G F 11 2 2 1 G ? ? ? ? ? Coulomb’s force F C = 2 2 1 o r q q 4 1 ?? = 9 × 10 9 04 . 0 q 2 Since, F G = F c = 04 . 0 q 10 9 04 . 0 2500 10 7 . 6 2 9 11 ? ? ? ? ? ? ? q 2 = 25 10 9 10 7 . 6 04 . 0 2500 10 7 . 6 9 9 11 ? ? ? ? ? ? ? ? = 18.07 × 10 –18 q = -18 10 18.07 ? = 4.3 × 10 -9 C. m 1 = 1 gm m 2 = 1 gm r Chapter-4 4.2 5. The limb exerts a normal force 48 N and frictional force of 20 N. Resultant magnitude of the force, R = 2 2 ) 20 ( ) 48 ( ? = 400 2304 ? = 2704 = 52 N 6. The body builder exerts a force = 150 N. Compression x = 20 cm = 0.2 m ?Total force exerted by the man = f = kx ? kx = 150 ? k = 2 . 0 150 = 2 1500 = 750 N/m 7. Suppose the height is h. At earth station F = GMm/R 2 M = mass of earth m = mass of satellite R = Radius of earth F= 2 ) h R ( GMm ? = 2 R 2 GMm ? 2R 2 = (R + h) 2 ? R 2 – h 2 – 2Rh = 0 ? h 2 + 2Rh – R 2 = 0 H = 2 R 4 R 4 R 2 2 2 ? ? ? ? ? ? ? ? ? = 2 R 2 2 R 2 ? ? = –R ± R 2 = R ? ? 1 2 ? = 6400 × (0.414) = 2649.6 = 2650 km 8. Two charged particle placed at a sehortion 2m. exert a force of 20m. F 1 = 20 N. r 1 = 20 cm F 2 = ? r 2 = 25 cm Since, F = 2 2 1 o r q q 4 1 ?? , F ? 2 r 1 2 1 2 2 2 1 r r F F ? ? F 2 = F 1 × 2 2 1 r r ? ? ? ? ? ? ? ? = 20 × 2 25 20 ? ? ? ? ? ? = 20 × 25 16 = 5 64 = 12.8 N = 13 N. 9. The force between the earth and the moon, F= G 2 c m r m m F = ? ? 2 8 24 22 11 10 8 . 3 10 6 10 36 . 7 10 67 . 6 ? ? ? ? ? ? ? = ? ? 16 2 35 10 8 . 3 10 36 . 7 67 . 6 ? ? ? = 20.3 × 10 19 =2.03 × 10 20 N = 2 ×10 20 N 10. Charge on proton = 1.6 × 10 –19 ? F electrical = 2 2 1 o r q q 4 1 ? ?? = ? ? 2 38 2 9 r 10 6 . 1 10 9 ? ? ? ? mass of proton = 1.732 × 10 –27 kg 48N x F F Chapter-4 4.3 F gravity = 2 2 1 r m m G = ? ? 2 54 11 r 10 732 . 1 10 67 . 6 ? ? ? ? ? ? ? ? ? 2 54 11 2 38 2 9 g e r 10 732 . 1 10 67 . 6 r 10 6 . 1 10 9 F F ? ? ? ? ? ? ? ? ? ? = ? ? ? ? 65 2 29 2 10 732 . 1 67 . 6 10 6 . 1 9 ? ? ? ? = 1.24 × 10 36 11. The average separation between proton and electron of Hydrogen atom is r= 5.3 10 –11 m. a) Coulomb’s force = F = 9 × 10 9 × 2 2 1 r q q = ? ? ? ? 2 11 2 19 9 10 3 . 5 10 0 . 1 10 9 ? ? ? ? ? ? = 8.2 × 10 –8 N. b) When the average distance between proton and electron becomes 4 times that of its ground state Coulomb’s force F = ? ? 2 2 1 o r 4 q q 4 1 ? ?? = ? ? ? ? 22 2 2 19 9 10 3 . 5 16 10 6 . 1 10 9 ? ? ? ? ? ? ? = ? ? ? ? 7 2 2 10 3 . 5 16 6 . 1 9 ? ? ? ? = 0.0512 × 10 –7 = 5.1 × 10 –9 N. 12. The geostationary orbit of earth is at a distance of about 36000km. We know that, g ? = GM / (R+h) 2 At h = 36000 km. g ? = GM / (36000+6400) 2 ? 0227 . 0 106 106 256 42400 42400 6400 6400 g ` g ? ? ? ? ? ? ? g ? = 0.0227 × 9.8 = 0.223 [ taking g = 9.8 m/s 2 at the surface of the earth] A 120 kg equipment placed in a geostationary satellite will have weight Mg` = 0.233 × 120 = 26.79 = 27 N * * * *Read More
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