A man weighing 80 kg is standing in a trolley weighing 320 kg. The trolley is resting on frictionless horizontal rails. If the man starts walking on the trolley with a speed of 1 m/s, then after 4 sec his displacement relative to the ground will be

1. 5  m

2. 4.8 m

3. 3.2 m

4. 3.0 m

If the body is moving in a circle of radius r with a constant speed v, its angular velocity is:

1. v²/r

2. vr

3. v/r

4. r/v

Two racing cars of masses \(m_1\) and \(m_2\) are moving in circles of radii \(r_1\) and \(r_2\) respectively. Their speeds are such that each makes a complete circle in the same duration of time \(t\). The ratio of the angular speed of the first to the second car is:
1. \(m_1:m_2\)
2. \(r_1:r_2\)
3. \(1:1\)
4. \(m_1r_1:m_2r_2\)

If a particle moves in a circle describing equal angles in equal times, its velocity vector:

(1) remains constant.

(2) changes in magnitude.

(3) changes in direction.

(4) changes both in magnitude and direction.

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

(1) R/r

(2) r/R

(3) R²/r²

(4) r²/R²

A particle is moving in a horizontal circle with constant speed. It has constant 

(1) Velocity

(2) Acceleration

(3) Kinetic energy

(4) Displacement

The angular speed of a flywheel making 120 revolutions/minute is: 

(1) $2\pi rad/s$

(2) $4{\pi }^{2}rad/s$

(3) $\pi rad/s$

(4) $4\pi rad/s$

An electric fan has blades of length 30 cm as measured from the axis of rotation. If the fan is rotating at 1200 r.p.m, the acceleration of a point on the tip of the blade is about

(1) 1600 m/sec²

(2) 4740 m/sec²

(3) 2370 m/sec²

(4) 5055 m/sec²

The angular speed of seconds needle in a mechanical watch is:

(1) $\frac{\pi }{30}$ rad/s

(2) 2π rad/s

(3) π rad/s

(4) $\frac{60}{\pi }$ rad/s

What is the value of linear velocity if \(\overset{\rightarrow}{\omega} = 3\hat{i} - 4\hat{j} + \hat{k}\) and \(\overset{\rightarrow}{r} = 5\hat{i} - 6\hat{j} + 6\hat{k}\)  :