Free Fall

Q. Water droplets are coming from an open tap at a particular rate. The spacing between a droplet observed at $4^{\text{th}}\text{second}$ after its fall, to the next droplet, is $34.3\text{m}.$ At what rate the droplets are coming from the tap ? (Take $g=9.8{\text{m/s}}^2$)

Q.

What do you mean by the term acceleration due to gravity? Explain the meaning of the following statement acceleration due to gravity is 9.8 ms^-2.

Q.

A hot air balloon is ascending at the rate 42 m/s and is 80 m above the ground when a package is dropped over the side. (a) How long does the package take to reach the ground? (b) With what speed does it hit the ground?

1. t = 15s, u = - 58 m/s

2. t = 10 s, u = - 58 m/s

3. $t=\frac{8}{5}s,u=12.8m/s$

4. t = 10 s, u = 58 m/s

Q. A helicopter is rising up from ground with an acceleration of $g{\text{m/s}}^2$, starting from rest after raising a height $h$ it attains a velocity of $v\text{m/s}$. At this instant, a particle is now released from the helicopter. Take $t=0$ at releasing time, calculate the time $t$ when particle reaches to the ground.

1. $\sqrt{\frac{2h}{g}}$
2. $2\sqrt{\frac{2h}{g}}$
3. $(1+\sqrt{2})\sqrt{\frac{2h}{g}}$
4. $4\sqrt{\frac{2h}{g}}$

Q. A ball thrown vertically upwards at a certain speed from the top of a tower, reaches the ground after $9\text{seconds}$. Another ball thrown vertically downwards with same speed from the same tower reaches the ground in $4$ seconds. How much time will the ball take if it is just dropped from the tower?

1. $6s$
2. $7s$
3. $5s$
4. $8s$

Q. An iron ball and a wooden ball of the same radius are released from the same height in vaccum. They take the same time to reach the ground. The reason for this is

1. Acceleration due to gravity in vaccum is same irrespective of the size and mass of the body.
2. Acceleration due to gravity in vaccum depend upon the mass of the body.
3. There is no acceleration due to gravity in vaccum.
4. In vaccum there is a resistance offered to the motion of the body and this resistance depends upon the mass of the body.

Q. With what speed should a body be thrown upwards so that the distances traversed in $5^{th}$ second and $6^{th}$ second are equal?

1. $5.84m/s$
2. $49m/s$
3. $\sqrt{98}m/s$
4. $98m/s$

Q. A ball is thrown vertically upward with a velocity of $10\text{m/s}$ from the top of a tower of height of $50\text{m}$. Find the time taken by the ball to reach a height $10\text{m}$ from the ground. (Take $g=10{\text{m/s}}^2$)

1. $1\text{s}$
2. $3\text{s}$
3. $4\text{s}$
4. $5\text{s}$

Q. The velocity of a ball vertically projected up is throughout its journey.

1. increasing
2. decreasing
3. decreasing and increasing

Q. A very large number of balls are thrown vertically upwards in quick succession in such a way that the next ball is thrown when the previous one is at the maximum height. If the maximum height is $5m$, the number of balls thrown per minute is $(takeg=10\frac{m}{s^2})$

1. 30
2. 60
3. 90
4. 45

Q. A ball is thrown vertically upward and its motion is studied before it falls on the ground. Which of the following represents velocity time graph of the ball during its flight (air resistance is neglected)

1. 
2. 
3. 
4. 

Q. A ball takes $t$ second to fall from a height $h_1$ and $2t$ seconds to fall from a height $h_2$. Then $\frac{h_1}{h_2}$ is:

1. $1.5$
2. $1$
3. $0.50$
4. $0.25$

Q.

A ball is thrown up from the top of a tower at 20 m/s velocity. It took the ball 6 sec to fall to the bottom. How high is the tower?

1. 20 m

2. 40 m

3. 30 m

4. 60 m

Q. A body undergoes a free fall. Taking downward direction as +ve $Y$ direction and $Y_o$ is the initial position, $Y$ coordinate at any time $t$ is given by

1. $Y_o-Y=\frac{1}{2}g{t}^2$
2. $Y_o=\frac{1}{2}g{t}^2$
3. $Y_o-Y=-\frac{1}{2}g{t}^2$
4. $Y_o+Y=\frac{1}{2}g{t}^2$

Q. When a ball is $h$ meter high from a point $O$, its velocity is $v_0$. When it is $h$meter below $O$, its velocity is $2v_0$. Find the maximum height from $O$ it will acquire

1. $\frac{2h}{3}$
2. $\frac{5h}{3}$
3. $\frac{3h}{2}$
4. $2h$

Q. A man bails out form an aeroplane and after dropping vertically through a distance of 40 m, he opens the parachute and decelerates at 2$m{s}^{-2}.$ If he reaches the ground with a speed of 2 𝑚/𝑠, how much distance did he travel in air ?

Q. Water drops are falling from a nozzle of a shower onto the floor, from a height of $9.8\text{m}$. The drops fall at a regular interval of time. When the first drop strikes the floor, at that instant, the third drop begins to fall. Locate the position of the second drop from the floor when the first drop strikes the floor.

1. $2.45\text{m}$
2. $7.35\text{m}$
3. $2.94\text{m}$
4. $4.18\text{m}$

Q. Two bodies of different masses are dropped from heights of $2\text{m}$ respectively, then the ratio of the time taken by them is

1. $1:4$
2. $1:1$
3. $1:2$
4. $1:3$

Q. A person throws balls into air after every second. The next ball is thrown when the velocity of the first ball is zero. How high do the ball rise above his hand?

1. $2m$
2. $5m$
3. $8m$
4. $10m$

Q.

A man in a balloon, throws a stone downwards with speed of 5 m/s with tespect ot balloon. The balloon is moving upwards with a constant acceleration of $5m/s^2$ . Then velocity of the stone relative to the man after 2 second is

1. 10 m/s

2. 30 m/s

3. 15 m/s

4. 35 m/s

Q. A stone thrown upward with a speed $u$ from the top of a tower reaches the ground with a speed $4u$. The height of the tower is

1. $\frac{15u^2}{2g}$
2. $\frac{7u^2}{2g}$
3. $\frac{16u^2}{g}$
4. $\text{Zero}$

Q. A stone is allowed to fall from the top of a tower $80\text{m}$ high and at the same time another stone is projected vertically upwards from the ground with a velocity of $20\text{m/s}$ along the same line of motion. The two stones will meet after -

1. $2\text{s}$
2. $4\text{s}$
3. $8\text{s}$
4. $6\text{s}$

Q. A stone is dropped into a well of $45m$ depth. The sound of splash due to the stone striking the water surface in the wall is heard after $3.125s$. From the given data, the velocity of sound in air is $(g=10m/s^2)$

1. 320 $m/s$
2. 340 $m/s$
3. 360 $m/s$
4. None of these

Q. Two spherical balls having equal masses with radius of $5\text{cm}$ each are thrown upwards along the same vertical direction at an interval of $3\text{s}$ with the same initial velocity of $35\text{m/s}$, then these balls will collide at a height of ____ $\text{m}$.
(Take $g=10{\text{m/s}}^2$)

Q. From the foot of a tower $90\text{m}$ high, a stone is thrown up so as to reach the top of the tower with zero velocity. Two seconds later another stone is dropped from the top of the tower. Find when will two stones meet for the first time ?

1. $4.5\text{s}$
2. $1.7\text{s}$
3. $3.1\text{s}$
4. $2.8\text{s}$

Q.

A ball is dropped from a height of $5\text{m}$. Find the velocity with which it hits the ground.

1. $10\text{m/s}$

2. $\sqrt{-100}\text{m/s}$

3. $5\text{m/s}$

4. $10\text{m/s}$

Q. A body is thrown vertically upward from the top $A$ of tower. It reaches the ground in $t_{1}s$. If it is thrown vertically downwards from $A$ with the same speed it reaches the ground in $t_{2}s$. If it is allowed to fall freely from $A$, then the time it takes to reach the ground is given by

1. $t=\frac{t_1+t_2}{2}$
2. $t=\frac{t_1-t_2}{2}$
3. $t=\sqrt{t_1{t}_2}$
4. $t=\sqrt{\frac{t_1}{t_2}}$

Q. For an object dropped under gravity, what is the ratio of displacement after equal subsequent time intervals starting from rest?

1. $1:3:\mathrm{5...}$
2. $1:2:\mathrm{3...}$
3. $1:2:\mathrm{4...}$

Q. A ball is dropped from a height of $20\text{m}$. At the same instant, another ball is thrown upward from the ground with a speed of $20\text{m/s}$ along the same line. After what time will the two balls meet?

1. $4\text{s}$
2. $3\text{s}$
3. $1\text{s}$
4. $2\text{s}$

Q. Two bodies of different masses $m_a$ and $m_b$ are dropped from two different height $a$ and $b$. The ratio of the time taken by the two to cover these distances are

1. $a:b$
2. $b:a$
3. $\sqrt{a}:\sqrt{b}$
4. $a^2:b^2$