# Uniform Circular Motion

## Trending Questions

**Q.**A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first 2 sec it rotates through an angle θ1, in the next 2 sec it rotates through an additional angle θ2. The ratio of θ2θ1 is

- 2
- 3
- 1
- 5

**Q.**A tunnel is dug along the diameter of Earth.There is a particle of mass m at the centre of tunnel.The maximum velocity given to the particle, so that it just reaches the surface of earth is: (R is radius of Earth and M is the mass of the earth )

- √GMR
- √GM2R
- √2GMR
- Zero

**Q.**When a ceiling fan is switched on, it makes 10 revolutions in the first 3 seconds. Assuming a uniform angular acceleration, how many rotations it will make in the next 3 seconds?

- 10
- 20
- 40
- 30

**Q.**Total kinetic energy of solid sphere of mass m rolling with velocity v without slipping is

- 710mv2
- 107mv2
- 56mv2
- 75mv2

**Q.**A particle is moving along a circular path with a constant speed of 10 ms−1. What is the magnitude of the change in velocity of the particle, when it moves through an angle of 60∘ around the centre of the circle?

- 10 m/s
- Zero
- 10√2 m/s
- 10√3 m/s

**Q.**

A person of $80kg$ mass is standing on the rim of a circular platform of mass $200kg$ rotating about its axis at $5$ revolutions per minute (rpm). The person now starts moving towards the center of the platform. What will be the rotational speed (in rpm) of the platform when the person reaches its center _____?

**Q.**A charged particle of specific charge α is released from origin at time t=0 with velocity →v=v0(^i+^j) in magnetic field →B=B0 ^i. The coordinate of the particle at time t=πB0α will be

- (v0πB0α, 0, −2v0B0α)
- (0, 2v0πB0α, 2v0B0α)
- (3v0πB0α, −2v0B0α, 0)
- (2√2v0πB0α, v0πB0α, √2v0B0α)

**Q.**

When a body moves with a constant speed along a circle

No acceleration is produced in the body

No work is done on it

No force acts on the body

Its velocity remains constant

**Q.**The seconds hand of a watch has length 6 cm. Speed of the end point and magnitude of difference in velocities at positions A and B, as shown in the figure will be

- 2π mms, 2√2π mms
- π mms, 2√2π mms
- 2π mms, √2π mms
- π mms, √2π mms

**Q.**

If a body is moving at constant speed in a circular path, its

velocity is constant and its acceleration is zero

velocity and acceleration are both changing directions only

velocity and acceleration are both increasing

velocity is constant and acceleration is changing direction

**Q.**A particle is projected vertically up with velocity v=4gR/3 from earth surface. The velocity of particle at height equal to half of maximum height reach by it

**Q.**A particle describes a horizontal circle in a conical funnel whose inner surface is smooth with speed of 0.5 m/s. What is the height of the plane of circle from vertex of the funnel?

- 0.25 cm
- 2 cm
- 4 cm
- 2.5 cm

**Q.**If a particle moves in a circle describing equal angles in equal intervals of times, its velocity vector

- Changes both in magnitude and direction
- Remains constant
- Changes in magnitude
- Changes in direction

**Q.**A stone tied to a string is rotated with a uniform speed in a vertical plane. If mass of the stone is m, the length of the string is r and the linear speed of the stone is v, when the stone is at its lowest point, then the tension in the string will be (g= acceleration due to gravity)

- mv2r−mg
- mvr
- mv2r+mg
- mg

**Q.**A charged particle of mass m and charge q is accelerated through a potential difference of V. It enters a region of uniform magnetic field B, which is directed perpendicular to the direction of motion of the particle. The particle will move on a circular path of radius given by -

- √Vm2qB2
- √Vm3qB2
- √2Vmq×(1B)
- √Vmq×(1B)

**Q.**A particle starting from rest rotates in a circle of radius R=√2 m with an angular acceleration α=π4 rad/sec2. The magnitude of average velocity of the particle over the time in rotating a quarter of a circle is

- 1 m/s
- 2 m/s
- 4 m/s
- 6 m/s

**Q.**An unbalanced force acts on a body. The body must

- remain at rest.
- move with uniform velocity.
- be accelerated.
- Can't predict

**Q.**

A hemisphere ball of radius R is set rotating about its axis of symmetry which is kept vertical. A small block kept in the bowl rotates with the bowl without slipping on its surface. If the surface of the bowl is smooth and the angle made by the radius through the block with the vertical is θ, find the angular speed at which the bowl is rotating.

- ω=√gcosθR
- ω=√gsecθR
- ω=√2gcosθR
- ω=√2gRsecθ

**Q.**A positively charged particle of specific charge (qm) is projected from the origin of coordinate with initial velocity (u^i−v^j). Uniform electric and magnetic fields exist in the region along the +y−direction, of magnitude E and B. The particle will definitely return to the origin once if

- uBπE is an integer
- vBπE is an integer
- (u2+v2)1/2BπE is an integer
- vB2πE is an integer

**Q.**Three identical particles are joined together by a thread as shown in figure. All the three particles are moving in a horizontal plane in circular path with O as centre. If the velocity of the outermost particle v0, then the ratio of tensions in the three sections of the string is

- 3:5:7
- 3:4:5
- 7:11:6
- 3:5:6

**Q.**The position vector of a particle is →r=a[cosωt^i+sinωt^j]. The velocity of the particle is

- parallel to position vector
- directed towards origin
- directed away from origin
- perpendicular to position vector.

**Q.**A body whose speed is constant -

- must be accelerated
- may be accelerated
- never be accelerated
- None of these

**Q.**In the figure a ball of mass m is tied with two strings of equal length as shown. If the rod is rotated with angular velocity ω and T1, T2 be tension in the strings as shown, then

- T1>T2
- T2>T1
- T1=2T2
- T1=T2

**Q.**When a particle moves in a uniform circular motion, it has

- radial velocity and radial acceleration.
- tangential velocity and radial acceleration.
- tangential velocity and tangential acceleration.
- radial velocity and tangential acceleration.

**Q.**Velocity and acceleration vectors of a charged particle moving in a magnetic field at some instant are →v=3^i+4^j and →a=2^i+x^j (Select the correct alternative(s).

- x=−1.5
- x=3
- Magnetic field is along z - direction.
- Kinetic energy of the particle is constant

**Q.**

An athlete completes one round of a circular track of diameter 14m with a uniform speed of 11m/s. Find the time taken.

**Q.**A simple pendulum with bob of mass m and conducting wire of length L swings under gravity through an angle θ. The component of earth's magnetic field, in a direction perpendicular to swing is B. Then

- The maximum velocity of pendulum is 2√gLsin(θ2)
- The maximum velocity of pendulum is √gLsin(θ2)
- The maximum potential difference induced across the pendulum is BL√gLsin(θ2)
- The maximum potential difference induced across the pendulum is 2BL√gLsin(θ2)

**Q.**A body is suspended from a spring balance kept in a satellite. The reading of the balance is W1 when the satellite goes in a an orbit of radius R and is W2 when it goes in an orbit or radius 2R.

- W1=W2

- W1<W2

- W1>W2

- W1≠W2

**Q.**

A particle moves with constant angular velocity in a circle. During the motion its

Energy is conserved

Momentum is conserved

Energy and momentum both are conserved

None of the above is conserved

**Q.**

The average acceleration vector for a particle having a uniform circular motion is

A constant vector of magnitude v2r

A vector of magnitude v2rdirected normal to the plane of the given uniform circular motion

Equal to the instantaneous acceleration vector at the start of the motion

A null vector