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:

Two blocks A and B of masses 4 kg and 12 kg are placed on a smooth plane surface. A force F of 16 N is applied on A as shown. The force of contact is :

1. 4 N

2. 8 N

3. 12 N

4. 16 N

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

Two particles of equal masses are revolving in circular paths of radii r₁ and r₂ respectively with the same speed. The ratio of their centripetal forces is 

1. $\frac{r_2}{r_1}$

2. $\sqrt{\frac{r_2}{r_1}}$

3. ${\left(\frac{{\displaystyle r_1}}{{\displaystyle r_2}}\right)}^2$

4. ${\left(\frac{{\displaystyle r_2}}{{\displaystyle r_1}}\right)}^2$

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 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