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 $\mathrm{m}/{\mathrm{s}}^2$

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:

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

A body of 5 kg is moving with a velocity of 20 m/s. If a force of 100 N is applied on it for 10 sec in the same direction as its velocity, what will now be the velocity of the body?

(1) 200 m/s

(2) 220 m/s

(3) 240 m/s

(4) 260 m/s

A cyclist turns around a curve at 15 miles/hour. If he turns at double the speed, the tendency to overturn is  

(1) Doubled

(2) Quadrupled

(3) Halved

(4) Unchanged

If the overbridge is concave instead of being convex, the thrust on the road at the lowest position will be

(1) $mg+\frac{m{v}^2}{r}$

(2) $mg-\frac{m{v}^2}{r}$

(3) $\frac{m^2{v}^{2}g}{r}$

(4) $\frac{v^{2}g}{r}$

A motor cyclist moving with a velocity of 72 km/hour on a flat road takes a turn on the road at a point where the radius of curvature of the road is 20 meters. The acceleration due to gravity is 10 m/sec². In order to avoid skidding, he must not bend with respect to the vertical plane by an angle greater than 

(1) $\theta ={\tan }^{-1}6$

(2) $\theta ={\tan }^{-1}2$

(3) $\theta ={\tan }^{-1}25.92$

(4) $\theta ={\tan }^{-1}4$

A particle moves in a circular orbit under the action of a central attractive force inversely proportional to the distance ‘r’. The speed of the particle is 

(1) Proportional to r²

(2) Independent of r

(3) Proportional to r

(4) Proportional to 1/r