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

1.		2.
3.		4.	None of these

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 forces \(F\) and \(2F\) are applied to both the blocks \(A\) and \(B\) respectively as shown in the figure. Block \(A\) does not slide on block \(B\). Then the normal reaction acting between the two blocks is:

1. \(F\)

2. \(\dfrac{F}{2}\)
3. \(\dfrac{F }{ \sqrt 3}\)
4. \(3F\)

Five persons \(A,\ B,\ C,\ D\ \text{and}\ E \) are pulling a cart of mass \(100\ \text{kg}\) on a smooth surface, and the cart is moving with an acceleration \(3 \ \text{m /s} ^ 2\) in the East direction. When person \(A\) stops pulling, it moves with an acceleration \(1 \ \text{m /s}^ 2\) in the west direction. When person\(​​B\) stops pulling, it moves with an acceleration \(24 \ \text{m/s}^ 2\) in the north direction. The magnitude of the acceleration of the cart when only \(A\) and\(​​B\) pull the cart, keeping their directions the same as the old directions, is:

1. \(26 \ \text{m/s}^ 2\)
2. \(3\sqrt{71} \ \text{m/s}^ 2\) $\mathrm{}$
3. \(25 \ \text{m/s}^ 2\)
4. \(30 \ \text{m/s}^ 2\)

A body moves along an uneven surface with constant speed at all points. The normal reaction due to ground on the body is:

The force required to just move a body up an inclined plane is double the force required to just prevent it from sliding down. If \(\phi\) is the angle of friction and \(\theta\) is the angle which the plane makes with the horizontal, then:
1. \(\tan 𝜃=\tan \phi\)

2. \(\tan 𝜃=2\tan \phi\)$$

3. \(\tan 𝜃=3\tan \phi\)$$

4. \(\tan \phi=\tan \theta\)$$

If the overbridge is concave instead of being convex, the thrust on the road at the lowest position will be:
1. \(mg+\dfrac{mv^2}{r}\)
2. \(mg-\dfrac{mv^2}{r}\)
3. \(\dfrac{mv^2g}{r}\)
4. \(\dfrac{v^2g}{r}\)

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 \(r^2\)

2. Independent of \(r\)

3. Proportional to \(r\)

4. Proportional to \(\dfrac 1r\)