Motion Under Gravity

Q.

A ball is thrown vertically upwards with a velocity of 20m/s from the top of a multi storey building.The height of the point from where the ball is thrown is 25m from the ground.

(a)How high will the ball rise

(b)How long will it be before the ball hits the ground.

Take g=10m/s

Q. If a ball is thrown vertically upwards with speed $u$, the distance covered during the last $t$ seconds of its ascent is

1. $ut-\frac{1}{2}g{t}^2$
2. $\frac{1}{2}g{t}^2$
3. $(u-gt)t$
4. $ut$

Q.

A cricketer can throw a ball to the maximum horizontal distance of 100 m. How much high above the ground can the cricketer throw the same ball?

Q.

Define K.E. Give its example and derive $KE=\frac{1}{2}m{v}^2$.

Q.

A ball is thrown straight up. What is its velocity and acceleration at the top?

Q.

A body dropped from top of a tower fall through $60m$ during the last $2s$ of its fall. The height of tower is (take, $g=10m/s^2$)

1. $95m$

2. $60m$

3. $80m$

4. $90m$

Q. A body falls freely from the top of a tower. It covers $36$% of the total height in the last second before striking the ground level. The height of the tower is

1. $50\text{m}$
2. $75\text{m}$
3. $100\text{m}$
4. $125\text{m}$

Q. A ball is dropped from a bridge $122.5\text{m}$ high. After the first ball has fallen for $2$ second, a second ball is thrown straight down after it, what must be the initial velocity of the second ball, so that both the balls hit the surface of water at the same time?

1. $26.1\text{m/s}$
2. $9.8\text{m/s}$
3. $55.5\text{m/s}$
4. $49\text{m/s}$

Q. A body is thrown upward and reaches its maximum height. At that position

1. Its velocity is zero and its acceleration is also zero
2. Its acceleration is minimum
3. Its velocity is zero and acceleration is the acceleration due to gravity
4. Its velocity is zero but its acceleration is maximum

Q. When forces $F_1,F_2,F_3$ are acting on a particle of mass $m$ such that $F_2$ and $F_3$ are mutually perpendicular, then the particle remains stationary. If the force $F_1$ is now removed, then the acceleration of the particle is

1. $F_1/m$
2. $F_2/m$
3. $(F_2-F_3)/m$
4. $F_2{F}_3/m{F}_1$

Q. A body travels half of its total path in the last second of its fall from rest. If $t$ and $H$ are the time and height of its fall (take $g=10{\text{m/s}}^2$). Then,

1. $t=2.4\text{s}$
2. $t=3.4\text{s}$
3. $H=28.8\text{m}$
4. $H=58.3\text{m}$

Q.

A body falling from rest has a velocity v after it falls through a height h. The distance it has to fall for its velocity to be 2v is.

Q. From a tower of height $H$, a particle is thrown vertically upwards with a speed $u$. The time taken by the particle to hit the ground is $n$ times that taken by it to reach the highest point of its path. The relation between $H,u$ and $n$ is

1. $n^2{u}^2=2gH$
2. $(n-2{)}^2{u}^2=gH$
3. $n(n-2)u^2=2gH$
4. $(n-2)u^2=gH$

Q. A stone thrown upward with a speed $u$ from the top of the tower reaches the ground with a velocity $3u$. The height of the tower is

1. $3u^2/g$
2. $4u^2/g$
3. $6u^2/g$
4. $9u^2/g$

Q. With what speed should a body be thrown upwards so that the distance traversed in $5^{th}$ second and $6^{th}$ second are equal? (Take $g=9.8m/s^2$)

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

Q. A stone dropped from a certain height reaches ground in $5\text{sec}$. If it is dropped and stopped for infinitesimal time interval at $t=3\text{s}$, then time taken by the stone to reach the ground is

1. $6\text{s}$
2. $7.5\text{s}$
3. $6.5\text{s}$
4. $7\text{s}$

Q. A stone is dropped from a balloon going up with a uniform velocity of $5\text{m/s}.$ If the balloon was $60\text{m}$ high when the stone was dropped, find the height of balloon when the stone hits the ground. Take $g=10\text{m/s}$.

1. $60\text{m}$
2. $80\text{m}$
3. $100\text{m}$
4. $50\text{m}$

Q.

A particle starts its motion from rest under the action of a constant force. If the distance covered in first $10seconds$ is $S_1$ and that covered in the first $20seconds$ is $S_2$ then

1. $S_2=2S_1$

2. $S_2=3S_1$

3. $S_2=4S_1$

4. $S_2=S_1$

Q.

How can you account for the fact that a stone and a feather fall at the same rate in vacuum but at different rate in air ?

Q. A ball is dropped vertically from a height $d$ above the ground. It hits the ground and bounces up vertically to a height $d/2$. Neglecting subsequent motion and air resistance, its velocity $v$ varies with height $h$ above the ground as.

1. 
2. 
3. 
4. 

Q.

What is Relative Motion?

Q. An object projected vertically up from the earth's surface with velocity $\sqrt{gR}$, where $R$ is the radius of the earth and $g$ is the acceleration due to gravity on the surface of earth. Find the maximum height reached by the object.

1. $R$
2. $2R$
3. $R/2$
4. $R/4$

Q. Strain is a unitless quantity. Why?

Q. Drops of water fall at regular intervals from the roof of a building of height $H=16\text{m}$. The first drop strikes the ground at the same moment when the fifth drop detaches itself from the roof. The distances between the different drops in air as the first drop reaches the ground are

1. $1\text{m},4\text{m},9\text{m},16\text{m}$
2. None of the above
3. $1\text{m},4\text{m},7\text{m},10\text{m}$
4. $1\text{m},3\text{m},5\text{m},7\text{m}$

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. A person standing near the edge of the top of a building throws two balls $A$ and $B$. The ball $A$ is thrown vertically upwards and $B$ is thrown vertically downward with the same speed. The ball $A$ hits the ground with a speed $v_A$ and the ball $B$ hits the ground with a speed $v_B$. Then,

1. $v_A>v_B$
2. $v_A<v_B$
3. $v_A=v_B$
4. The relation between $v_A$ and $v_B$ depends on height of the building above the ground.

Q. From the top of a tower, a stone is thrown up and reaches the ground in time $t_1$ . A second stone is thrown down with the same speed and reaches the ground in time $t_2$. A third stone is released from rest and reaches the ground in time $t_3$ -

1. $t_3=\frac{1}{2}(t_1+t_2)$
2. $t_3=\sqrt{t_1{t}_2}$
3. $\frac{1}{t_3}=\frac{1}{t_2}-\frac{1}{t_1}$
4. $t_3^2=t_1^2-t_2^2$

Q. A stone dropped from a building of height $h$ and it reaches the ground after $t$ seconds. From the same building if two stones are thrown (one upwards and other downwards) with the same velocity $u$ and they reach the ground after $t_1$ and $t_2$ seconds respectively, then

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

Q.

What does a negative force mean?

Q.

A particle is projected vertically upwards in absence of air resistance with a velocity u from a point O. When it returns to the point of projection:

(1) Its a average velocity is zero

(2) Its displacement is zero

(3) Its average speed is $\frac{u}{2}$

(4) Its average speed is u

1. 1 and 2 are correct

2. 1, 2 and 3 are correct

3. 3 and 4 are correct

4. only 4 is correct