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:

The forces required to just move a body up an inclined plane is double the force required to just prevent it from sliding down. If $\mathrm{\varphi }$ is angle of friction and $\mathrm{\theta }$ is the angle which the plane makes with horizontal, then

1. $\tan \theta =\tan \varphi$

2. $\tan \theta =2\tan \varphi$

3. $\tan \theta =3\tan \varphi$

4. $\tan \varphi =3\tan \theta$

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

Two masses M and m are attached to a vertical axis by weightless threads of combined length l. They are set in rotational motion in a horizontal plane about this axis with constant angular velocity ω. If the tensions in the threads are the same during motion, the distance 'x' of M from the axis is- 

1. $\frac{Ml}{M+m}$

2. $\frac{ml}{M+m}$

3. $\frac{M+m}{M}l$

4. $\frac{M+m}{m}l$

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.

Three identical particles are joined together by a thread as shown in figure. All the three particles are moving in horizontal circles centred at O. If the velocity of the outermost particle is v₀, then the ratio of tensions in the three sections of the string is 

1. 3 : 5 : 7

2. 3 : 4 : 5

3. 7 : 11 : 6

4. 3 : 5 : 6

A bucket full of water is revolved in vertical circle of radius 2m. What should be the maximum time-period of revolution so that the water doesn't fall off the bucket ?

1. 1 sec

2. 2 sec

3. 3 sec

4. 4 sec

A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity ω. The force exerted by the liquid at the other end is 

1. $\frac{ML{\omega }^2}{2}$

2. $ML{\omega }^2$

3. $\frac{ML{\omega }^2}{4}$

4. $\frac{M{L}^2{\omega }^2}{2}$