J J Science Academy

1) A ball rolls from the top of a stair way with a horizontal velocity $(u m / s)$. If the steps are h m high and b m wide, the ball will hit the edge of the $(n^{th})$ step, if

1) $(n=\frac{2 h u}{g b^{2}})$ 2) $(n=\frac{2 h u^{2}}{g b^{2}})$ 3) $(n=\frac{2 h u^{2}}{g b})$ 4) $(n=\frac{h u^{2}}{g b^{2}})$

Hint:

$(nh=\frac{1}{2} gt^{2} \quad nb=ut)$ From these two equation we get, $$nh=\frac{g}{2}(\frac{nb}{u})^{2}$$ $$n=\frac{2 hu^{2}}{gb^{2}}$$

2) A body rolls down a stair case of 5 steps. Each step has height 0.1 m and width 0.1 m . With what velocity will the body reach the bottom?

1) $(5 \sqrt{2} m / s)$ 2) $(\frac{1}{\sqrt{2}} m / s)$ 3) $(2 \sqrt{2} m / s)$ 4) $(\sqrt{\frac{5}{2}} m / s)$

Hint:

Horizontal distance covered by the body $(5 \times 0.1=0.5 m)$ Vertical distance covered by the body $(5 \times 0.1=0.5 m)$ If the time taken to hit the edge of $(5^{th})$ step is t,then

3) A bomb is dropped from an aeroplane moving horizontally at constant speed. When air resistance is taken into consideration, the bomb

1) falls to earth exactly below the aeroplane. 2) fall to earth behind the aeroplane. 3) falls to earth ahead of the aeroplane. 4) flies with the aeroplane.

Hint:

Due to air resistance, horizontal velocity of bomb will decrease so it will fall behind the aeroplane.

4) A ball rolls off the edge of a horizontal plane 4.9 m high. If it strikes the floor at a point 10 m horizontally away from the edge of the plane, speed of the ball at the instant it left the plane is

1) $(10 ms^{-1})$ 2) $(20 ms^{-1})$ 3) $(30 ms^{-1})$ 4) $(40 ms^{-1})$

Hint:

If $(t)$ is the time of flight of the ball, then $$t=\sqrt{\frac{2 h}{g}}=\sqrt{\frac{2 \times 4.9}{9.8}}=1 s$$ Horizontal distance covered, $$x=ut$$ $$10=u \times 1$$ $$u=10 m / s$$

5) A bomb is dropped, from a plane moving at an altitude H , with a speed u . The angle at which the target should appear to it, so as to hit it, is

1) $(\tan ^{-1}(\frac{1}{2} \sqrt{\frac{gH}{u^{2}}}))$ 2) $(\tan ^{-1}(\sqrt{\frac{2 gH}{u^{2}}}))$ 3) $(\tan ^{-1}(\sqrt{\frac{gH}{u^{2}}}))$ 4) $(\tan ^{-1}(\sqrt{\frac{gH}{2 u^{2}}}))$

Hint:

$$H=\frac{1}{2} gt^{2} \Rightarrow t=\sqrt{\frac{2 H}{g}}$$ $$v_{Y}=g t=g \sqrt{\frac{2 H}{g}}=\sqrt{2 g H}$$ $$v_{X}=u$$ $$tan \theta=\frac{v_{Y}}{v_{X}}=\sqrt{\frac{2 gH}{u^{2}}}$$ $$theta=\tan ^{-1}(\sqrt{\frac{2 gH}{u^{2}}})$$

6) A bomb is dropped, from a plane moving at an altitude H , with a speed u . The velocity with which the bomb strikes the target is

1) $(\sqrt{u^{2}+g H})$ 2) $(\sqrt{u^{2}+2 g H})$ 3) $(\sqrt{2 gH})$ 4) u

Hint:

$$v_{net }=\sqrt{v_{X}^{2}+v_{Y}^{2}}=\sqrt{u^{2}+2 g H}$$

7) Two identical bullets, $(B_{1})$ and $(B_{2})$, are fired horizontally with different velocities $(v_{1})$ and $(v_{2},(v_{1}>v_{2}))$ from the same height. Which will reach the ground with greater momentum?

1) }\mp@subsup{B}{1}{ 2) $(B_{2})$ 3) Both will reach with same momentum. 4) It cannot be predicted