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. $79~\text{gm}$