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1.  The length of a spring is \(l_1\) and \(l_2\) when stretched with a force of \(4\) N and \(5\) N respectively. Its natural length is?

1.	\(l_2+l_1\)	2.	\(2(l_2-l_1)\)
3.	\(5l_1-4l_2\)	4.	\(5l_2-4l_1\)

2.

The value of \(M\) of the hanging block is in the figure, which will prevent the smaller block (\(m\)\(=\)\(1\) kg) from slipping over the triangular block. All the surfaces are smooth and string and pulley are ideal. (Given: \(M'\)\(=4\) kg and \(\theta\) \(=37^\circ\))
           
1. \(12\) kg
2. \(15\) kg
3. \(10\) kg
4. \(4\) kg

3. When a \(5\) kg plastic box is placed deep inside the water, it accelerates up at a rate of \(\dfrac{g}{6}\). How much sand should be put inside the box so that it may accelerate down at the rate of \(\dfrac{g}{6}\)?

1.	\(2~\text{kg}\)	2.	\(3~\text{kg}\)
3.	\(4~\text{kg}\)	4.	\(5~\text{kg}\)

4.

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

5.

A particle is moving in a vertical circle. The tension in the string when passing through two positions at angle of 30$°$ and 60$°$ from vertical (the lowest position) are ${\mathrm{T}}_1 \mathrm{and} {\mathrm{T}}_2$ respectively, then:
1.  ${\mathrm{T}}_1 = {\mathrm{T}}_2$
2.  ${\mathrm{T}}_2 < {\mathrm{T}}_1$
3.  ${\mathrm{T}}_2 > {\mathrm{T}}_1$
4.  Tension in the string always remains the same.

6.

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. \(g \downarrow ,   0\)
$\mathrm{}$

7.

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 $\mathrm{m}/{\mathrm{s}}^2$

8.

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

1.	maximum at \(A\)
2.	maximum at \(B\)
3.	minimum at \(C\)
4.	the same at \(A, B\) and \(C\)

9.

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.

10.

A long horizontal rod has a bead which can slide along its length, and initially placed at a distance L from one end A of the rod. The rod is set in angular motion about A with constant angular acceleration $\alpha$. If the coefficient of friction between the rod and the bead is μ, and gravity is neglected, then the time after which the bead starts slipping is
(1) $\sqrt{\frac{\mu }{\alpha }}$
(2) $\frac{\mu }{\sqrt{\alpha }}$
(3) $\frac{1}{\sqrt{\mu \alpha }}$
(4) Infinitesimal

11.

A mass of 1 kg is suspended by a string A. Another string C is connected to its lower end (see figure). If a sudden jerk is given to C, then

(1) The portion AB of the string will break
(2) The portion BC of the string will break
(3) None of the strings will break
(4) The mass will start rotating

12.

A machine gun is mounted on a 2000 kg car on a horizontal frictionless surface. At some instant the gun fires bullets of mass 10 gm with a velocity of 500 m/sec with respect to the car. The number of bullets fired per second is ten. The average thrust on the system is 
(1) 550 N
(2) 50 N
(3) 250 N
(4) 250 dyne

13.

A lift accelerated downward with acceleration 'a'. A man in the lift throws a ball upward with acceleration a₀ (a₀ < a). Then acceleration of ball observed by an observer, which is on earth, is 
(1) (a + a₀) upward
(2) (a – a₀) upward
(3) (a + a₀) downward
(4) (a – a₀) downward

14.

A string of negligible mass going over a clamped pulley of mass \(m\) supports a block of mass \(M\) as shown in the figure. The force on the pulley by the clamp is given by:
 
1. \(\sqrt{2} M g\)
2. \(\sqrt{2} m g\)
3. \(g\sqrt{\left( M + m \right)^{2} + m^{2}}\)
4. \(g\sqrt{\left(M + m \right)^{2} + M^{2}}\)

15.

A block \(B\) is placed on top of block \(A\). The mass of block \(B\) is less than the mass of block \(A\). Friction exists between the blocks, whereas the ground on which block \(A\) is placed is assumed to be smooth. A horizontal force \(F\), increasing linearly with time begins to act on \(B\). The acceleration \(a_A\) and \(a_B\) of blocks \(A\) and \(B\) respectively are plotted against \(t\). The correctly plotted graph is:

1.		2.
3.		4.