A rod of length L and mass m is acted on by two unequal forces $F_1$ and $F_2\left(<F_1\right)$ as shown in the following figure

The tension in the rod at a distance y from the end A is given by :

1. $F_1\left(1-\frac{y}{L}\right)+F_2\left(\frac{y}{L}\right)$

2. $F_2\left(1-\frac{y}{L}\right)+F_1\left(\frac{y}{L}\right)$

3. $\left(F_1-F_2\right)\frac{y}{L}$

4. None of the above

Two blocks A and B of masses m & 2m respectively are held at rest such that the spring is in natural length. Find the accelerations of both the blocks just after release.

(1) $g\downarrow , g\downarrow$

(2) $\frac{g}{3}\downarrow , \frac{g}{3}\uparrow$

(3) (0, 0)

(4) $g\downarrow , 0$

Two blocks 'A' and 'B' each of mass 'm' are placed on a smooth horizontal surface. Two horizontal force F and 2F are applied on both the blocks 'A' and 'B' respectively as shown in figure. The block A does not slide on block B. Then the normal reaction acting between the two blocks is:

(1) F

(2) F/2

(3) $\frac{F}{\sqrt{3}}$

(4) 3F

Five persons A, B, C, D & E are pulling a cart of mass 100 kg on a smooth surface and the cart is moving with acceleration 3 $\mathrm{m}/{\mathrm{s}}^2$ in east direction. When person 'A' stops pulling, it moves with acceleration 1 $\mathrm{m}/{\mathrm{s}}^2$ in the west direction. When person 'B' stops pulling, it moves with acceleration 24 $\mathrm{m}/{\mathrm{s}}^2$ in the north direction. The magnitude of the acceleration of the cart when only A & B pull the cart keeping their directions same as the old directions are:

1.  26 $\mathrm{m}/{\mathrm{s}}^2$

2.  $3\sqrt{71} \mathrm{m}/{\mathrm{s}}^2$

3.  25 $\mathrm{m}/{\mathrm{s}}^2$

4.  30 $\mathrm{m}/{\mathrm{s}}^2$

A body moves along an uneven surface with constant speed at all points. The normal reaction due to ground on the body is:

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 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 made by the rod with the track is

1.  Zero

2.  30$°$

3.  45$°$

4.  60$°$

The engine of a car produces an acceleration of 4 m/s² in the car. If this car pulls another car of the same mass, what will be the acceleration produced?

(1) 8 m/s²

(2) 2 m/s²

(3) 4 m/s²

(4) $\frac{1}{2}m/s^2$   

A truck and a car are moving with equal velocity. If equal retarding force is applied on each, then on applying the brakes both will stop after certain distance 

(1) Truck will cover less distance before rest

(2) Car will cover less distance before rest

(3) Both will cover equal distance

(4) None

A constant force acts on a body of mass 0.9 kg at rest for 10s. If the body moves a distance of 250 m, the magnitude of the force is 

(1) 3 N

(2) 3.5 N

(3) 4.0 N

(4) 4.5 N