While walking on ice one should take small steps to avoid slipping. This is because smaller steps ensure

1. Larger friction

2. Smaller friction

3. Larger normal force

4. Smaller normal force

A block is kept on a rough inclined plane with angle of inclination $\theta$. The graph of net reaction (R) versus $\theta$ is:

1.		2.
3.		4.	None of these

A block is placed on a rough horizontal plane. A time dependent horizontal force F=kt acts on the block. The acceleration time graph of the block is :

1.		2.
3.		4.

A motorcycle is going on an overbridge of radius R. The driver maintains a constant speed. As the motorcycle is ascending on the overbridge, the normal force on it:

1.  Increases

2.  decreases

3.  remains the same

4.  fluctuates erratically

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:

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: