The length of a spring is  \(l_1\) and \(l_2\) when stretched with a force of 4 N and 5 N respectively. Its natural length is?

1.	\(l_2+l_1\)	2.	\(2(l_2-l_1)\)
3.	\(5l_1-4l_2\)	4.	\(5l_2-4l_1\)

 

When a 5 kg plastic box is placed deep inside water, it accelerates up at a rate of g/6. How much sand should be put inside the box so that it may accelerate down at the rate of g/6?

Two masses, m and M, are connected by a light string passing over a smooth pulley. When mass m moves up by 1.4 m in 2 sec, the ratio $\frac{m}{M}$ is:

A heavy uniform chain partly lies on a horizontal table. If the coefficient of friction between the chain and the table surface is 0.25, then the maximum fraction of the length of the chain that can hang over the edge of the table will be:

1. 20 %

2. 25 %

3. 33 %

4. 15 %

A ball of mass 0.1 Kg is whirled in a horizontal circle of radius 1 m by means of a string at an initial speed of 10 rpm. Keeping the radius constant, the tension in the string is reduced to one quarter of its initial value. The new speed is:

A point mass m is suspended from a light thread of length l, fixed at O, and is whirled in a horizontal circle at a constant speed as shown. From your point of view, stationary with respect to the mass, the forces on the mass are:

1.		2.
3.		4.

A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m/sec. A plumb bob is suspended from the roof of the car by a light rigid rod of length 1.00 m. The angle formed by the rod with respect to the vertical is:

A particle moves in the XY-plane under the action of a force F such that the components of its linear momentum p at any time t are \(p_x = 2 \cos t\),  \(p_y = 2 \sin t\) . The angle between F and p at time t will be:

A lift is going up. The total mass of lift and the passenger is \(1500\) kg. The variation in the speed of the lift is as given in the graph. The tension in the rope pulling the lift at \(t=11^{\text{th}}\) s will be:

      
1. \(17400\) N
2. \(14700\) N
3. \(12000\) N
4. zero

The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle \(\theta\) should be: 
     
1. \(0^\circ\)
2. \(30^\circ\)
3. \(45^\circ\)
4. \(60^\circ\)