A non-uniform bar of weight \(W\) is suspended at rest by two strings of negligible weight as shown in the figure. The angles made by the strings with the vertical are \(36.9^\circ\) and  \(53.1^\circ\) respectively. The bar is \(2\) m long. The distance \(d\) of the center of gravity of the bar from its left end is:
(Take sin\(36.9^\circ=0.6\) and sin\(53.1^\circ=0.8\))

           
1. \(69\) cm
2. \(72\) cm
3. \(79\) cm
4. \(65\) cm

A car weighs \(1800~\text{kg}.\) The distance between its front and back axles is \(1.8~\text m.\) Its center of gravity is \(1.05~\text m,\) behind the front axle. The force exerted by the level ground on each front wheel and each back wheel is respectively:
1. \(2680~\text N, ~5145~\text N\)
2. \(5145~\text N, ~3675~\text N\)
3. \(5145~\text N, ~5145~\text N\)
4. \(3675~\text N, ~5145~\text N\)

A rope of negligible mass is wound around a hollow cylinder of mass \(3\) kg and radius \(40\) cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of \(30\) N?
(Assume that there is no slipping.)
1. \(21\) rad/s²
2. \(24\) rad/s²
3. \(20\) rad/s²
4. \(25\) rad/s²

To maintain a rotor at a uniform angular speed of \(200~\text{rad/s},\) an engine needs to transmit a torque of \(180~\text{N-m}.\) What is the power required by the engine?
1.  \(33~\text{kW}\)
2.  \(36~\text{kW}\)
3.  \(28~\text{kW}\)
4.  \(76~\text{kW}\)

A meter stick is balanced on a knife edge at its center. When two coins, each of the mass \(5\) gm are put one on top of the other at the \(12.0\) cm mark, the stick is found to be balanced at \(45.0\) cm. What is the mass of the meter stick?
1. \(66~\text{gm}\) 
2. \(56~\text{gm}\) 
3. \(76~\text{gm}\) 
4. \(79~\text{gm}\)