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. \(\text F\)

2. \(\text F /2\)
3. \(F \over \sqrt 3\)
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:

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.