Staircase Equivalence to an Incline

Q. A body falling freely from a given height $H$, hits an inclined plane in its path at a height $h$. As a result of this impact the direction of velocity of the body becomes horizontal. For what value of $\frac{h}{H}$ will the body take maximum time to reach the ground?

1. $\frac{1}{2}$
2. $\frac{1}{4}$
3. $\frac{3}{4}$
4. $1$

Q. A wicketkeeping glove is dropped from a height of $40\text{m}$ and simultaneously a ball is thrown upwards from the ground with a speed of $40\text{m/s}$. When will they meet?

$(g=10{\text{m/s}}^2)$

1. $1\text{s}$ after glove is dropped
2. $2\text{s}$ after glove is dropped
3. $3\text{s}$ after glove is dropped
4. $4\text{s}$ after glove is dropped

Q. A standing man, observes rain falling with velocity of $20m/s$ at an angle of ${30}^{\circ }$ with the vertical. Find the velocity with which the man should, moves so that rain appears to fall vertically to him.

1. $20m/s$
2. $16m/s$
3. $10m/s$
4. $7m/s$

Q. A body falling freely from a given height $H$, hits an inclined plane in its path at a height $h$. As a result of this impact the direction of velocity of the body becomes horizontal. For what value of $\frac{h}{H}$ will the body take maximum time to reach the ground?

1. $\frac{1}{2}$
2. $\frac{1}{4}$
3. $1$
4. $\frac{3}{4}$

Q. From the top of tower of height 100 m a 10 gm block is dropped freely and a 6 gm bullet is fired vertically upward from the foot of the tower with velocity 100 $m{s}^{-1}$ simultaneously. They collide and stick together after time. Find the time after which they collide with each other.

Q. Initially, a balloon has $2g$ of air inside it. A small hole is pierced into it. The air comes out with a velocity of $4m/s$. If the balloon shrinks completely in $2.5s$, the average pressure acting on the balloon is:

1. $0.008N$
2. $0.0032N$
3. $8N$
4. $3.2N$

Q. A body falling freely from a given height $H$, hits an inclined plane in its path at a height $h$. As a result of this impact the direction of velocity of the body becomes horizontal. For what value of $\frac{h}{H}$ will the body take maximum time to reach the ground?

1. $\frac{1}{2}$
2. $\frac{1}{4}$
3. $\frac{3}{4}$
4. $1$

Q. A body falling freely from a given height $H$, hits an inclined plane in its path at a height $h$. As a result of this impact the direction of velocity of the body becomes horizontal. For what value of $\frac{h}{H}$ will the body take maximum time to reach the ground?

1. $\frac{1}{2}$
2. $\frac{1}{4}$
3. $1$
4. $\frac{3}{4}$

Q. Two practicles are projected simultaneously from the same point on ground at angle ${73}^o$ and ${53}^o$ with horizontal with speed $V$ and $2V$ in the same vertical plane, then relative velocity between them when both are in air (neglect the air resistance).

1. Is always vertical
2. Is changing continuously
3. Is constant
4. Becomes zero once

Q. A smooth inclined plane having angle of inclination ${30}^0$ with horizontal has a mass 2.5 kg held by a spring which is fixed at the upper end as shown in figure. If the mass is taken 2.5 cm up along the surface of the inclined plane, the tension in the spring reduces to zero. If the mass is then released, the angular frequency of oscillation in radian per second is

1. 0.707
2. 7.07
3. 1.414
4. 14

Q. A body falling freely from a given height $H$, hits an inclined plane in its path at a height $h$. As a result of this impact the direction of velocity of the body becomes horizontal. For what value of $\frac{h}{H}$ will the body take maximum time to reach the ground?

1. $\frac{1}{2}$
2. $\frac{1}{4}$
3. $1$
4. $\frac{3}{4}$