Centripetal Force and Circular Motion

Q. A particle is acted upon by a constant force, the magnitude of which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. Which of the following can be true for the particle?

1. Its velocity is changes.
2. Its magnitude of acceleration is constant
3. (b) and (c) above.
4. Its speed remains same and it is in circular motion

Q.

The time period of a satellite of the earth is $5h$. If the separation between the earth and the satellite is increased to $4$ times the previous value, the new time period will become

1. $40h$

2. $20h$

3. $10h$

4. $80h$

Q. A stone of mass $m$ is rotated in a circular path with a uniform speed by tying a strong string with the help of your hand. Answer the following questions:
(i) Is the stone moving with a uniform or variable speed?
(ii) Is the stone moving with a uniform acceleration? In which direction does the acceleration act?
(iii) What kind of force acts on the hand and state its direction?

Q.

For a body in uniform circular motion, (if we are rotating a stone using our hand tied by a thread ) which all real forces act ? The centripetal force will be because of the tension in the string, but which is the real force that causes the circular motion as centripetal (tension) force acts inwards . so which Real force causes such a motion( as centrifugal force is only imaginary )

Q. Centripetal force is given by the formula

1. $F=m{v}^2/R$
2. $F=mvR$
3. $F=mv/R$
4. $F=m{v}^3/R$

Q.

A car is moving at a constant speed of 70 km/h. Which of the following statements is correct?

1. The acceleration of the car is definitely zero.

2. The car has an acceleration only if it is moving along a curved path

3. The car may have an acceleration even if it is moving along a straight path

4. The car may not have an acceleration even if it is moving along a curved path

Q.

A centripetal force acts

1. radially inwards

2. radially outwards

3. tangentially

4. axially

Q.

What is a Centripetal force?

Q.

Define 1-newton force.

Q. If a car drives along a circular racetrack at a constant speed of $80km{h}^{-1}$, then the car is accelerating.

1. True
2. False

Q.

A mass is supported on a frictionless horizontal surface. It is attached to a string and rotates fixed center at an angular velocity ${\omega }_0$ . If the length of the string and angular velocity both are doubled, the tension in the string which was initially $T_0$ is now​

Q.

What will happen to a car moving on a circular path if the friction between the car and the road suddenly disappears?

1. It will skid along the radius outwards

2. It will skid along the radius inwards

3. It will skid along the tangent

4. It will skid towards the centre of the circular road

5. It will skid along the radius in the same direction as it is travelling

Q.

How do you calculate orbital speed?

Q. If a force equal to half the weight of the body can just move the body on a plane surface then the coefficient of friction is

Q. ___ is the average distance between the center of the sun, measured from the center of the earth.

Q. One end of string of length $l$ is connected to a particle of mass '$m$' and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed '$v$', the net force on the particle (directed towards center) will be ($T$ represents the tension in the string)

1. Zero
2. $T+\frac{m{v}^2}{l}$
3. $T$
4. $T-\frac{m{v}^2}{l}$

Q. A body is revolving with a constant speed along a circular path. Which of the following statements are true regarding that body?

1. Its acceleration is directed along the axis of revolution
2. If the direction of velocity is reversed, the centripetal force does not change in magnitude and direction
3. If the direction of velocity is reversed, the centripetal force does not change in magnitude but its direction changes
4. Its velocity changes due to change of direction

Q. Obtain an expression for acceleration of a performing uniform circular motion.

Q.

A uniform sphere of mass $M$ and radius $R$ exerts a force $F$ on a small mass $m$ situated at a distance of $2R$ from the centre $O$ of the sphere. A spherical portion of diameter $R$ is cut from the sphere as shown in the figure. The force of attraction between the remaining part of the sphere and the mass $m$ will be:

1. $\frac{2F}{3}$

2. $\frac{7F}{9}$

3. $\frac{4F}{9}$

4. $\frac{F}{3}$

Q. A body revolves with constant speed v in a circular path of radius r . the magnitude of its average acceleration during motion between two points in diametrically opposite direction is:

1. Zero
2. $\frac{v^2}{r}$
3. $\frac{2v^2}{\pi r}$
4. $\frac{v^2}{2r}$

Q. An insect trapped in circular groove of radius 12 cm moves along the groove steadily and completes revolutions in 100 s. (a) What is the angular speed of motion? (b) Is the acceleration vector constant ? What is its magnitude?

Q. The wheel starting from rest is rotating with a constant angular acceleration $3rad/s^2$, the radius of wheel is $0.5m$. The centripetal acceleration of the particle on the rim at end of $2$ seconds is

1. $10m/s^2$
2. $15m/s^2$
3. $18m/s^2$
4. $12m/s^2$

Q. When a body is moving along a circular track, the force directed towards the centre of the track is called

1. centripetal force
2. centrifugal force
3. gravitational force

Q. A car moves with constant speed of $10m/s$ in a circular path of radius $10$m. The mass of the car is $1000$kg. Who or what is providing the required centripetal force for the car? How much is its?

Q. A particle moves in a circle of radius $2.0cm$ at a speed given by $v=4t$, where $v$ is in cm/s and $t$ is in seconds. Find total acceleration at $t=1s$.

1. $4\sqrt{5}cm/s^2$
2. $2\sqrt{5}cm/s^2$
3. $4\sqrt{3}cm/s^2$
4. $4cm/s^2$

Q. The earth (mass = $6\times {10}^{24}$ kg), revolves around the sun with an angular velocity of $2\times {10}^7$ rad/s, in a circular orbit of radius $1.5\times {10}^8$ km. The force exerted by the sun on the earth is:

1. $zero$
2. $18\times {10}^{20}$ N
3. $27\times {10}^{30}$ N
4. $3.6\times {10}^{22}$ N

Q. A stone of mass $1kg$ is whirled in horizontal circle attached at the end of a 1 m long string. If the string makes an angle of ${30}^o$ with vertical, calculate the centripetal force acting on the stone.$(g=9.8m/s^2)$. (in $N$)

1. $5.369$
   
2. $5.658$
   
3. $5.123$
   
4. $6.321$
   

Q. A body of mass $5$kg is moving in a circle of radius $1$ m with an angular velocity of $2$ rad/sec. Then the centripetal force will be

1. 20 N
2. 30 N
3. 80 N
4. 10 N

Q. Work done by the centripetal force is always .....................

1. zero
2. non of these
3. Infinity
4. more than zero

Q.

You have a bag of cotton and an iron bar, each indicating a mass of 100 kg when measured on a weighing machine. In reality, one is heavier than other. Can you say which one is heavier and why? Define mass. Is it scalar or vector quantity?
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