Free Fall

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. How to derive the velocity time relation and position time relationfor a uniformly accelerated motion by graphical method

Q.

Escape velocity of a body of 1 kg mass on a planet is 100 m/sec. Gravitational Potential energy of the body at the Planet is

1. - 5000 J

2. - 1000 J

3. - 2400 J

4. 5000 J

Q. Show that area under the velocity time curve of a body moving uniformly gives the displacement of the particle in a given time.

Q.

Two balls of different masses are thrown vertically upwards with the same speed. They pass through the point of projection in their downward motion with the same speed (Neglect air resistance). Is it possible?

Q.

A U tube of uniform bore of cross-sectional area A has been set up vertically with open ends facing up. Now m gm of a liquid of density d is poured into it. The column of liquid in this tube will oscillate with a period T such that

1. 

2. 

3. 

4. 

Q.

The radius and mass of earth are increased by 0.5%. Which of the following statements are true at the surface of the earth

1. g will increase

2. g will decrease

3. Escape velocity will remain unchanged

4. Potential energy will remain unchanged

Q.

The gravitational force between two stones of mass 1 kg each separated by a distance of 1 metre in vacuum is

1. 

2. 

3. 

4. Zero

Q.

why there is no gravity at centre of earth?

Q. Show that the instantaneous velocity of a particle at any instant is equal to slope of tangent drawn to displacement-time curve at that instant.

Q. percentage decrease in the value of acceleration due to gravity on moving 32 km above the earth surface wrt earths surface is (take radius of earth 6400) 1. 0.5% 2. 1% 3.1.5% 4.2

Q.

A force of 15 N is acting on a particle of mass 3 kg towards north and a force of 20 N is acting on another particle of mass 2 kg towards east. The acceleration of the centre of mass of the two particle system is

1. 7 m/s²

2. 17 m/s²

3. 55 m/s²

4. 5 m/s²

Q. If the radius of the earth shrinks by 2%, mass remaining cons†an t , then how would the value of acceleration due to gravity change ?

Q.

The speed of efflux from an open tank is given by a formula identical to that of a:

1. freely falling body

2. recoiling gun

3. liquid flowing in a horizontal pipe

4. projectile

Q. The acceleration due to gravity of the ball at the highest point, considering downwards as negative, is $-9.8{\text{m/s}}^2$

1. True
2. False

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

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

Q. When a mass $2\text{kg}$ is shifted from infinity to a point in gravitational field, it is found that work done by external force is $-100\text{J}$. If the mass is doubled and taken again from the same point to infinity without accelerating it, then the work done by gravitational force will be

1. $-200\text{J}$
2. $400\text{J}$
3. $-100\text{J}$
4. $200\text{J}$

Q. what does the area of an acceleration-displacement graph of a uniformly accelerated body represent

Q. A: the acceleration due to gravity for an object is independent from its mass. R: the value of g depends on mass of the planet

Q. A body falling from rest has a velocity ${}^{\prime }{v}^{\prime }$ after it falls through a distance ${}^{\prime }{h}^{\prime }$. The distance it has to fall down further, for its velocity to become $3v,$ is

1. $4h$
2. $8h$
3. $3h$
4. $6h$

Q. Acceleration of ball inside water

Q. A body dropped from the top of a tower falls through $40m$ during the last two seconds of its fall. The height of tower is $(g=10m/s^2)$

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

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 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? For how long was the ball above the tower?

1. 1 sec

2. 4 sec

3. 6 sec

4. 2 sec

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. The speed-time graph of a particle moving along a fixed direction is shown in Fig. Obtain the distance traversed by the particle between time t = 0 s to 10 s.

Q. When a ball is thrown vertically upwards with velocity $v_0$, it reaches a maximum height of $h$. If one wishes to triple the maximum height then the ball should be thrown with velocity.

1. $\sqrt{3}{v}_0$
2. $3v_0$
3. $9v_0$
4. $\frac{3}{2}{v}_0$

Q. The relation between time $t$ and distance $x$ for a moving body is given as $t=m{x}^2+nx$, where $m$ and $n$ are constants. The retardation of the motion is :
$\left(\text{Where}v\text{stands for velocity}\right)$

1. $2m{v}^3$
2. $2mn{v}^3$
3. $2n{v}^3$
4. $2n^2{v}^3$

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 stone is thrown vertically upward with an initial velocity $v_o.$ The distance travelled in time $\frac{1.5v_o}{g}$ is

1. $\frac{v_o^2}{2g}$
2. $\frac{3v_o^2}{8g}$
3. $\frac{5v_o^2}{8g}$
4. None of these