Uniformly accelerated motion relations
- A bullet from a gun is fired on a rectangular wooden block with velocity u. When bullet travels 24 cm through the block along its length horizontally, velocity of bullet becomes u/3. Then it further penetrates into the block in the same direction bef… Answer: 2. 27 cm Assume a constant resistive force, so deceleration a is constant. Use v²=u²-2as . First 24 cm: (u/3)²=u²-2a(24)⇒ 48a=8u²/9⇒... 1
- A horizontal bridge is built across a river. A student standing on the bridge throws a small ball vertically upwards with a velocity 4 m s^-1. The ball strikes the water surface after 4 s. The height of bridge above water surface is (Take g=10 m s^-2… Answer: 4. 64 m Take upward as positive. The ball starts with u=+4 m/s, and its displacement at the water is -h after 4 s. s=ut-1/2gt²⇒ -h=4... 1
- The ratio of the distances travelled by a freely falling body in the 1^st, 2^nd, 3^rd and 4^th second : Answer: 4. 1 : 3 : 5 : 7 For a body falling from rest, the distance in the n th second is s_n=1/2g(2n-1) . So the distances in 1st, 2nd, 3rd... 1
- A small block slides down on a smooth inclined plane, starting from rest at time t = 0. Let S_n be the distance travelled by the block in the interval t = n − 1 to t = n. Then, the ratio S_nS_n+1 is : Answer: 2. 2n-1/2n+1 Key idea: distance in the n-th second from rest is S_n=1/2a(2n-1) . S_n∝(2n-1) and S_(n+1)∝(2n+1) , so dfracS_nS_(n+1)=... 1
- A ball is thrown vertically downward with a velocity of 20 m/s from the top of a tower. It hits the ground after some time with a velocity of 80 m/s. The height of the tower is : (g = 10 m/s^2) Answer: 4. 300 m Use v²=u²+2gh (downward motion, g positive). h=v²-u²/2g=80²-20²/2×10=6400-400/20=300\ m Answer: option 4. 1
- When an object is shot from the bottom of a long smooth inclined plane kept at an angle 60^° with horizontal, it can travel a distance x_1 along the plane. But when the inclination is decreased to 30^° and the same object is shot with the same veloci… Answer: 3. 1:√(3) On a smooth incline the retardation is gsinθ . For the same launch speed v , the distance up the plane is x=v²/2gsinθ , so... 1