Dropping Objects

Q. A stone falls freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first three second of its motion. The stone remains in the air for

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

Q. A body dropped from the top of a tower covers a distance $7x$ in the last second of its journey where $x$ is the distance covered in first second. How much time does it take to reach the ground (Take $g=10{m/s}^2$)?

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

Q. Two bodies $A$ (of mass 1 kg) and $B$ (of mass 3 kg) are dropped from height of 16 m and 25 m, respectively. The ratio of the time taken by them to reach the ground is

1. $\frac{4}{5}$
2. $\frac{5}{4}$
3. $\frac{12}{5}$
4. $\frac{5}{12}$

Q. Two particles 1 and 2 are allowed to descend on two frictionless chords $OA$ and $OB$ of a vertical circle, at the same instant from point $O$. The ratio of the velocities of 1 and 2 respectively, when they reach the circumference will be ($OB$ is the diameter)

1. $\cos \alpha$
2. $\sin \alpha$
3. $\tan \alpha$
4. none of these

Q. A stone is dropped from a bridge and it reaches the ground in $4$ seconds. The height of the bridge is

1. $78.4\text{m}$
2. $64.2\text{m}$
3. $98.6\text{m}$
4. $116.8\text{m}$

Q. A particle moves in a circle of radius 25 cm at two revolutions per sec. The acceleration of the particle in $m/s^2$ is :

1. $\pi$
2. $8{\pi }^2$
3. $4{\pi }^2$
4. $2{\pi }^2$

Q.

Why does a railway track have a particular shape I ?

Q. A stone is dropped into a well in which the level of water is $h$ below the top of the well. If $v$ is velocity of sound, the time $T$ after which the splash is heard is given by

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

Q.

In a resonance tube experiment, a closed organ pipe of length 120 cm resonates when tuned with a tuning fork of frequency 340 Hz. If water is poured in the pipe, then (velocity of sound in air is 340 m/s)

1. Minimum length of water column to have the resonance is 45 cm
2. The distance between two successive nodes is 50 cm
3. The maximum length of water column to create the resonance is 95 cm
4. The maximum length of water column to create the resonance is 45 cm

Q.

The escape velocity of the earth is $11.2\frac{km}{s}$. What is the escape velocity on a planet whose radius is twice that of the earth and mass four times that of the earth?

Q. A stone is dropped into a well in which the level of water is $h$ below the top of the well. If $v$ is speed of sound in the air, the time $T$ after which the splash is heard is given by

1. $T=\frac{2h}{v}$
2. $T=\sqrt{\frac{2h}{g}}+\frac{h}{v}$
3. $T=\sqrt{\frac{2h}{g}}+\frac{h}{2v}$
4. $T=\sqrt{\frac{h}{2g}}+\frac{2h}{v}$

Q. A balloon is moving vertically with a velocity of $4\text{m/s}$. When it is at a height of $h$, a ball is gently released from it. If it reaches the ground in $4\text{s}$, the height of the balloon when the body is released is

1. $96\text{m}$
2. $64\text{m}$
3. $78\text{m}$
4. $80\text{m}$

Q. A body falling from a high Minaret travels 40 meters in the last 2 seconds of its fall to ground. Height of Minaret in meters is (take g=10 $m/s^2$)

1. 60
2. 45
3. 80
4. 50

Q. A man bails out from an aeroplane and after dropping vertically through a distance of 40 $m$, he opens parachute and decelerates at 2$m/s^2.$ If he reaches ground with speed of 2 𝑚/𝑠, how much distance did he travel in air?
($g=9.8m/s^2$)

1. $215m$
2. $235m$
3. $250m$
4. $195m$

Q. Two balls $A$ and $B$ of the same size are dropped from the same point under gravity. If the air resistance acting on both the balls is same and the mass of $A$ is greater than the mass of $B$, then

1. $\text{The ball}A\text{reaches earlier.}$
2. $\text{Cannot say, as the data is insufficient.}$
3. $\text{The ball}B\text{reaches earlier.}$
4. $\text{Both the balls reach the ground simultaneously.}$

Q. A man standing on the roof of a house of height h throws one particle vertically downwards and another particle horizontally with the same velocity u. The ratio of their velocities when they reach the earth’s surface will be

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

Q. A body dropped from the top of a tower covers the distance $7x$ in the last second of its journey, where $x$ is the distance covered in $1\text{st}$ sec. How much time does it take to reach the ground ?

1. $3\text{sec}$
2. $4\text{sec}$
3. $5\text{sec}$
4. $6\text{sec}$

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. A sandbag ballast is dropped from a balloon that is ascending with a velocity of $40ft/s$. If the sandbag reaches the ground in $20s$, how high was the balloon when the bag was dropped? Neglect air resistance.

1. $5260ft$
2. $6000ft$
3. $5000ft$
4. $5760ft$

Q. A point moves along a circle with velocity $v=at,$ where $a=0.5{\text{m/s}}^2$. Then the total acceleration of the point at the moment, when it has covered ${\left(\frac{1}{10}\right)}^{th}$ of the circle after the beginning of motion is

1. $0.5{\text{m/sec}}^2$
2. $0.6{\text{m/sec}}^2$
3. $0.7{\text{m/sec}}^2$
4. $0.8{\text{m/sec}}^2$

Q. A stone falls from a balloon that is descending at a uniform rate of $12\text{m/s}$. The displacement of the stone from the point of release after $10\text{sec}$ is

1. $490\text{m}$
2. $610\text{m}$
3. $725\text{m}$
4. $510\text{m}$

Q. Ball $A$ is dropped from the top of a building. At the same instant, ball $B$ is thrown vertically upwards from the ground. When the balls collide, they are moving in opposite directions and the speed of $A$ is twice the speed of $B$. At what fraction of the height of the building did the collision occur?

1. $1/3$
2. $2/3$
3. $1/4$
4. $2/5$

Q. A body is projected vertically upward with speed $40m/s$. The distance travelled by the body in last 2 second of the journey is $[g=10m/s^2]$

1. $5\text{m}$
2. $10\text{m}$
3. $60\text{m}$
4. $15\text{m}$

Q. A body falling for 2 seconds covers a distance S equal to that covered in next second. Taking $g=10m/s^2,S=$

1. 30 m
2. 60 m
3. 20 m
4. 10 m

Q.

A ball is dropped from a of height of 5m from ground. Find the velocity with which it hits the ground.

1. 5 m/s

2. 10 m/s

3. - 10 m/s

4. 

Q. From a tap $10m$ high, water drops fall at regular intervals. When the first drop reaches the ground, the $5^{th}$ drop is about to leave the tap. Find the separation between $2^{nd}$ and $3^{rd}$ drops.

1. $\frac{35}{8}m$
2. $\frac{31}{8}m$
3. $\frac{27}{8}m$
4. $\frac{25}{8}m$

Q. A body thrown vertically up with a finite speed is caught back after $4\text{sec}$. The speed of the body with which it is thrown up is
(Take $g=10{\text{m/s}}^2$)

1. $10\text{m/sec}$
2. $20\text{m/sec}$
3. $30\text{m/sec}$
4. $40\text{m/sec}$

Q.

A flower pot falls off a window sill and falls past the window below. It takes $0.5s$ to pass through a window that is $2.0\text{m}$ above the ground. Find how high is the window sill from the ground?

(Take $g=10m/s^2$)

1. $2.5\text{m}$
2. $2.25\text{m}$
3. $3.25\text{m}$
4. $4.5\text{m}$

Q. From the top of a tower of height $200\text{m}$, a ball A is projected up with $10{\text{ms}}^{-1}$ and $2\text{s}$ later another ball B is projected vertically down with the same speed. Then (Neglect air friction)

1. Both A and B will reach the ground simultaneously
2. Ball A will hit the ground, $2\text{s}$ after B hits the ground
3. Both the balls will hit the ground with the same velocity
4. Both the balls will hit the ground with the different velocity

Q.

Discuss mation of an object under free fall. Neglect air resistence.