For \(L = 3.0~\text{m,}\) the total torque about pivot \(A\) provided by the forces as shown in the figure is:

A constant torque of 1000 N-m turns a wheel of moment of inertial 200 $\mathrm{kg}-{\mathrm{m}}^2$ about an axis through its centre. Its angular velocity after 3 s is

1. 1 rad/s

2. 5 rad/s

3. 10 rad/s

4. 15 rad/s

An automobile engine develops 100 kW when rotating at a speed of 1800 rev/min. What torque does it deliver ?

1. 350 N-m

2. 440 N-m

3. 531 N-m

4. 628 N-m

In the following figure, a weight W is attached to a string wrapped round a solid cylinder of mass M mounted on a frictionless horizontal axle at O.

If the weight starts from rest and falls a distance h, then its speed at that instant is

1. Proportional to \(\text R\)

2. Proportional to \(1 \over R\)

3. Proportional to \(1 \over R^2\)

4. Independent of \(\text R\)

Assertion : A ladder is more apt to slip when you are high up on it than when you just begin to climb

Reason : At the high point on a ladder, the torque is large and on climbing up the torque is small