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1.

A block of mass 2 kg is lifted through a chain. When block moves through 2 m vertically the velocity becomes 4 m/s. Work done by chain force until it moves 2 m is: (g = $10 m/s^{-2}$)
 
1. 40 J
2. 24 J
3. 56 J
4. None of these

2.

A car comes to a skidding stop in 1 5m. The force on the car due to the road is 1000 N. The work done by road on the car and car on the road respectively is
 
1. -15 kJ, zero
2. zero, 15 kJ
3. 15 kJ, zero
4. -15 kJ, 15 kJ

3.

A particle is released from rest at origin. It moves under the influence of potential field $U=x^2-3x$, where $$$U$ is in Joule and $x$ is in metre. Kinetic energy at x = 2 m will be
 
1. 2 J
2. 1 J
3. 1.5 J
4. O J

4.

The potential energy of a particle of mass $m$ is giveil by $U=\frac{1}{2}k{x}^2$ for x < 0 and U = O for $x\ge 0$. If total mechanical energy of the particle is E. Then its speed at $x=\sqrt{\frac{2E}{k}}$ is
 
1. zero
2. $\sqrt{\frac{2E}{m}}$
3. $\sqrt{\frac{E}{m}}$
4. $\sqrt{\frac{E}{2m}}$

5.

Two springs A and B ($k_A$ = $2k_B$) are stretched by applying forces of equal magnitudes at the ends. If the energy stored in A is E, then energy stored in B is
1. $\frac{E}{2}$
2. 2$E$
3. $E$
4. $\frac{E}{4}$

6.

A body constrained to move in $\gamma$-direction is subjected to a force given by
$\stackrel{\rightharpoonup }{F}$ = $\left(-2\stackrel{\rightharpoonup }{i}+15\stackrel{\rightharpoonup }{j}+6\stackrel{\rightharpoonup }{k}\right)$N. The work done by this force in moving the body a distance of 10 m along the $\gamma$-axis is
 
1. 20 J
2. 150 J
3. 60 J
4. 190 J

7.

A variable force F starts acting on a block of mass 5 kg resting on a smooth horizontal surface. F is varying with displacement x as shown in F - x curve. The velocity of body when its displacement is 3m will be

1. 2$m{s}^{-1}$
2. $2\sqrt{2}m{s}^{-1}$
3. $2\sqrt{3}m{s}^{-1}$
4. 6$m{s}^{-1}$

8.

A force acts on a 3 gram particle such that its position $x=3t^2+t^3$, where $x$ is in metre and $t$ is in second. The work doue during first 4s is
 
1. 825 mJ
2. 285 mJ
3. 528 mJ
4. zero

9.

An object of mass 10 kg falls from rest through a vertical distance of 10 m and acquires a velocity of 10 m/s. The work done by the push of air on the object is (g = 10 m/$s^2$)
 
1. 500J
2. -500J
3. 250J
4. -250J

10.

The relationship between force and position is shown in figure (in one dimensional case). The work doue by the force in displacing a body from x = 1 cm to x = 5 cm is

1. 20 ergs
2. 60 ergs
3. 70 ergs
4. 700 ergs

11.

A position dependent force \( F = x^2 - 3 \) newton acts on a small body of mass 2 kg and displaces it from \( x = 0 \) to \( x = 5 \) m. The work done is:

1. 110 J
2. \( \frac{80}{3} \) J
3. \( \frac{95}{2} \) J
4. zero

12.

A body of mass m slides down a smooth curved track of same mass which is the quadrant of circle having radius 10 m. The speed of the body at the bottom of track is

1.  $10\sqrt{2}$ m/s
2.  10 m/s
3.  2 m/s
4.  20 m/s 

13.

A body of mass M is dropped from a height h on a sand floor. If the body penetrates x m into the sand, the average resistance offered by the sand to the body is
1. $Mg\left(\frac{h}{x}\right)$
2. $Mg\left(1+\frac{h}{x}\right)$
3. $Mgh+Mgx$
4. $Mg\left(1+\frac{h}{x}\right)$

14.

An object is thrown horizontally from a tower H ilieter high with a velocity of $\sqrt{2gH}$ m/s. Its velocity on striking the ground will be 
1. $\sqrt{2gH}$
2. $\sqrt{6gH}$
3. $2\sqrt{gH}$
4. $2\sqrt{2gH}$

15.

A particle slides on a frictionless elevated curved track from a point A which terminates in a straight horizontal section ending at C as shown. If the particle loses the contact with the track at C, the particle will hit hte ground from C at a horizontal distance of 

1.  0.5 m
2.  0.8 m
3.  1.0 m
4.  1.2 m

16.

The average power of the pump which lifts 20 kg of water per second from a well 10 ni deep and projects it with a velocity 10 m/s is (g = 10 m/$s^2$)
1. 9 kW
2. 4.5 kW
3. 2.5 kW
4. 3 Kw

17.

The potential energy of a body is given by. U = A - $B{x}^2$ (where x is the displacement). The inagiiitude of force acting on the particle is 
1. constant.
2. proportional to $x$.
3. proportional to $x^2$
4. inversely proportional to $x$.

18. The figure shows a smooth curved track ending in a smooth horizontal section. A spring with a spring constant of \(400\) N/m is attached to the horizontal part, as illustrated. A \(40\) g mass is released from rest at a height of \(4.9\) m on the curved track. What is the maximum compression of the spring?

1. \(4.9\) cm
2. \(9.8\) cm
3. \(19.6\) cm
4. none of these

19. The kinetic energy acquired by a body of mass \(M\) after traveling a fixed distance from rest under the action of a constant force is:
1. \(\propto M\)
2. \(\propto \sqrt M\)
3. \(\propto \frac1{\sqrt M}\)
4. independent of \(M\)

20.

The displacement $\chi$ of a body of mass 1 kg on horizontal smooth surface as a function of time  t is given by $\chi$ = $\frac{t^3}{3}$. The work done by the external agent for the first one second is
1. O.25 J
2. O.5 J
3. O.75 J
4. 1 J

21.

A particle of mass 0.1 kg is subjected to a force which varies with distance as shown in figure. If it starts its journey from rest at x = 0, its velocity at x = 12 m is

1. 0 m/s
2. $20\sqrt{2}$ m/s
3. $20\sqrt{3}$ m/s
4. 40 m/s

22.

The potential energy of a system is represented in the first figure.
The force acting on the system will be represented by 

 
1. 
2. 
3. 
4. 

23.

A bob is suspended from a crane by a cable of length $l$ = 5 m. The crane and the bob are moving at a constant speed $vo$. The crane is stopped by a bumper and the bob on the cable swings out an angle of ${60}^0$. The initial speed $vo$ is (g =9.8 $m/s^2$)
1. 10 m/s
2. 7 m/s
3. 4 m/s
4. 2 m/s

24.

The speed $\nu$ reached by a car of mass m, driven with a constant power P, is given by (where $x$ is displacement in meter)
 
1. $v=\frac{3xP}{m}$
2. $v={\left(\frac{3xP}{m}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$
3. $v={\left(\frac{3xP}{m}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$
4. $v={\left(\frac{3xP}{m}\right)}^2$

25.

The string of a pendulum of length $l$ is displaced through 60° from the vertical and
released. The minimum strength of the string in order to withstand the tension as the pendulum passes through the mean position is (mass of bob is m)
1. 2 mg
2. 3 mg
3. 5 mg
4. 6 mg