If two forces ($6\hat{\mathrm{i}}$ $+$ $8\hat{\mathrm{j}}$) and ($4\hat{\mathrm{i}}$ $+$ $4\hat{\mathrm{j}}$) N are acting on a body of mass 2 kg, then the acceleration produced in the body in $\mathrm{m}/{\mathrm{s}}^2$ will be:

1. ($5\hat{\mathrm{i}}$ $+$ $6\hat{\mathrm{j}}$)

2. ($10\hat{\mathrm{i}}$ $+$ $12\hat{\mathrm{j}}$)

3. ($6\hat{\mathrm{i}}$ $+$ $12\hat{\mathrm{j}}$)

4. ($2\hat{\mathrm{i}}$ $+$ $3\hat{\mathrm{j}}$)

The friction between the front foot and the back foot when walking on a horizontal surface is, respectively:

1. Forward, forward

2. Backward, backward

3. Forward, backward

4. Backward, forward

A simple pendulum hangs from the roof of a train moving on horizontal rails. If the string is inclined towards the front of the train, then the train is:

1. moving with constant velocity.

2. in accelerated motion.

3. in retarded motion.

4. at rest.

A block of mass M is pulled by a force F, making an angle $\mathrm{\theta }$ with the horizontal on a smooth horizontal surface as shown. If a is the acceleration of block on the surface, then the contact force between the block and the surface will be:
        
1. Mg + Macos$\mathrm{\theta }$

2. Mg - Macos$\mathrm{\theta }$

3. Mg + Matan$\mathrm{\theta }$

4. Mg - Matan$\mathrm{\theta }$

A body of mass m is moving on a concave bridge ABC of the radius of curvature R at a speed v. The normal reaction of the bridge on the body at the instant it is at the lowest point of the bridge is:

1.  $\mathrm{mg}$ $-$ $\frac{{\mathrm{mv}}^2}{\mathrm{R}}$

2.  $\mathrm{mg}$ $+$ $\frac{{\mathrm{mv}}^2}{\mathrm{R}}$

3.  mg

4.  $\frac{{\mathrm{mv}}^2}{\mathrm{R}}$

A block B of mass \(3\) kg is kept on block A of mass \(5\) kg in a lift accelerating upward with an acceleration of \(g.\) The reaction by A on B is:                                                 

If the force acting on a system is zero, the quantity which remains constant is:

Two blocks, A and B, of masses 2m and 4m are connected by a string. The block of mass 4m is connected by a spring (massless). The string is suddenly cut. The ratio of the magnitudes of accelerations of masses 2m and 4m at that instant will be:

The reading of spring balance in the depicted figure will be:

The angle of banking for a cyclist taking a turn at a curve is given by tan$\mathrm{\theta } = \frac{{\mathrm{v}}^{\mathrm{n}}}{\mathrm{rg}}$ where symbols have their usual meaning. The value of n is: