Centripetal Acceleration

Q. A simple pendulum has a length $l$, mass of bob $m$. The bob is given a charge $q$ coulomb. The pendulum is suspended in a uniform horizontal electric field of strength $E$ as shown in figure, then calculate the time period of oscillation when the bob is slightly displaced from its mean position:

1. $2\pi \sqrt{\frac{l}{g}}$
2. $2\pi \sqrt{\frac{l}{g+\frac{qE}{m}}}$
3. $2\pi \sqrt{\frac{l}{g-\frac{qE}{m}}}$
4. $2\pi \sqrt{\frac{l}{\sqrt{g^2+{\left(\frac{qE}{m}\right)}^2}}}$

Q.

One end of a string of length l is connected to a particle of mass m and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed v the net force on the particle (directed towards the centre) is:
(i) T,
(ii) $T-\frac{m{v}^2}{l}$
(iii) $T+\frac{m{v}^2}{l}$
(iv) 0
T is the tension in the string. [Choose the correct alternative].

Q. how far apart two protons be if the electrostatics force excerted by one on the other is equal to weight of electron

Q. The ratio of escape velocity on earth $\left(v_e\right)$ to the escape velocity on a planet $\left(v_p\right)$ whose radius and mean density are twice as that of earth is

1. $1:\sqrt{2}$
2. $1:2$
3. $1:2\sqrt{2}$
4. $1:4$

Q. A body is moving in a circular path with acceleration $a$. If its speed gets doubled, find the ratio of acceleration after and before the speed is changed

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

Q. Define non-uniform circular motion.

Q. In a "well of death", a person rides on the vertical face of a cylinder. The coefficient of friction between the tyres and the surface is ${}^{\prime }{\mu }^{\prime }$. Find the minimum velocity with which he should ride for him not to fall.

1. $\frac{gr}{\mu }$
2. $\sqrt{\frac{gr}{\mu }}$
3. $\sqrt{\frac{2gr}{\mu }}$
4. $\sqrt{\frac{gr}{2\mu }}$

Q.

A ball of mass 0.1 Kg. is whirled in a horizontal circle of radius 1 m. by means of a string at an initial speed of 10 R.P.M. Keeping the radius constant, the tension in the string is reduced to one quarter of its initial value. The new speed is

1. 5 r.p.m.

2. 14 r.p.m.

3. 10 r.p.m.

4. 20 r.p.m.

Q. define angular velocity and derive v=rw in detailed ste by step explanation

Q.

Two bodies of mass 10 kg and 5 kg moving in concentric orbits of radii R and rsuch that their periods are the same. Then the ratio between their centripetal acceleration is

1. $\frac{R^2}{r^2}$

2. $\frac{r^2}{R^2}$

3. $\frac{R}{r}$

4. $\frac{r}{R}$

Q. A simple pendulum of length $1\text{m}$ is oscillating with an angular frequency of $10\text{rad/s}.$ The support of the pendulum starts oscillating up and down with a small angular frequency of $1\text{rad/s}$ and an amplitude of ${10}^{-2}\text{m}$. The relative change in the angular frequency of the pendulum is best given by:

1. ${10}^{-3}\text{rad/s}$
2. $1\text{rad/s}$
3. ${10}^{-1}\text{rad/s}$
4. ${10}^{-5}\text{rad/s}$

Q.

Find the maximum velocity for skidding for a car moved on a circular track of radius 100 m. The coefficient of friction between the road and tyre is 0.2

1. 0.14 m/s

2. 14 m/s

3. 140 m/s

4. 1.4 km/s

Q.

A body of mass 1 kg tied to one end of string is revolved in a horizontal circle of radius 0.1 m with a speed of 3 revolution/sec, assuming the effect of gravity is negligible, then linear velocity, acceleration and tension in the string will be

1. $1.88m/s,35.5m/s^2,35.5N$

2. None of these

3. $2.88m/s,45.5m/s^2,45.5N$

4. $3.88m/s,55.5m/s^2,55.5N$

Q. Two stones of masses $m$ and $2m$ are whirled in horizontal circles. The heavier one is whirled in a circle of radius $\frac{r}{2}$ and the lighter one in a circle of radius $r$. The tangential speed of lighter stone is $n$ times that of the speed of heavier stone. If they experience the same centripetal forces, the value of $n$ is

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

Q. A disc revolves with a speed of $33\frac{1}{3}rev/min$ and has a radius of $15cm$. Two coins are placed at $4cm$ and $14cm$ away from the centre of the record. If the coefficient of friction between the coins and the record is $0.15$, which of the coin revolves with the record? Answer $1.00$ for the coin placed at $4cm$, $2.00$ for the coin placed at $14cm$ and $3.00$ for both coins.

Q.

A particle moves with constant speed v along a circular path of radius r and completes the circle in time T. The acceleration of the particle is

1. $\frac{2\pi v}{T}$

2. $\frac{2\pi r}{T}$

3. $\frac{2\pi r^2}{T}$

4. $\frac{2\pi v^2}{T}$

Q.

A mass of 2 kg is whirled in a horizontal circle by means of a string at an initial speed of 5 revolutions per minute. Keeping the radius constant the tension in the string is doubled. The new speed is nearly

1. 10 rpm

2. 2.25 rpm

3. 7 rpm

4. 14 rpm

Q.

A car sometimes overturns while taking a turn. When it overturns, it is

1. The inner wheel which leaves the ground first

2. The outer wheel which leaves the ground first

3. Both the wheels leave the ground simultaneously

4. Either wheel leaves the ground first

Q.

What can you say about the tangential and normal components of acceleration if the direction of velocity of a body is changing?

Q.

What is the acceleration of uniform circular motion?

Q.

A ball of mass 0.25 kg attached to the end of a string of length 1.96 m is moving in a horizontal circle. The string will break if the tension is more than 25 N. What is the maximum speed with which the ball can be moved

1. 3.92 m/s

2. 14 m/s

3. 3 m/s

4. 5 m/s

Q. A circular road of radius 1000 m has banking angle ${45}^{\circ }$. The maximum safe speed of a car having mass 2000 kg will be, if the coefficient of friction between tyre and road is 0.5

1. 172 m/s
2. 86 m/s
3. 124 m/s
4. 99 m/s

Q. A car of mass 1000kg moves on a circular track of radius 20m. If the coefficient of friction is 0.64, then the maximum velocity with which the car move is:

1. 6.5 m/s
2. 22.4 m/s
3. 5.6 m/s
4. 11.2 m/s

Q. A spotlight $S$ rotates in a horizontal plane with a constant angular velocity of $0.1rad{s}^{-1}$ The spot of light $P$ moves along the wall at a distance $3m$. What is the velocity of spot $P$ when $\theta ={45}^{\circ }$ ?

1. $0.1m{s}^{-1}$
2. $0.2m{s}^{-1}$
3. $0.4m{s}^{-1}$
4. $0.6m{s}^{-1}$

Q.

A body of mass 5 kg is moving in a circle of radius 1mwith an angular velocity of 2 radian/sec. The centripetal force is

1. 10 N

2. 30 N

3. 20 N

4. 40 N

Q.

A stone of mass 0.25 kg tied to the end of a string is whirled round in a circle of radius 1.5 m with a speed of 40 rev./min in a horizontal plane. What is the tension in the string?
What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of 200 N?

Q.

A cylindrical object of outer diameter 10 cm, height 20 cm and density 8000 kg $m^{-3}$ is supported by a vertical spring and is half dipped in water as shown in figure. (a) Find the elongation of the spring in equilibrium condition. (b) If the object is slightly depressed and released, find the time period of resulting oscillations of the object. The spring constant = 500 N $m^{-1}$

Q.

Name the force that is used to dry clothes in a washing machine.

Q.

A 100 kg car is moving with a maximum velocity of 9 m/s across a circular track of radius 30 m. The maximum force of friction between the road and the car is

1. 1000 N

2. 706 N

3. 200 N

4. 270 N

Q. A person with his hands in his pockets is skating on ice at the velocity of 10 m/s and describes a circle of radius 50 m. What is his inclination with vertical

1. $ta{n}^{-1}\left(\frac{1}{10}\right)$
2. $ta{n}^{-1}\left(\frac{3}{5}\right)$
3. $ta{n}^{-1}\left(1\right)$
4. $ta{n}^{-1}\left(\frac{1}{5}\right)$