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Question Bank No: 1

1. A particle is released from a height h at a certain height, Its K.E is two times its potential energy. Height and speed of the particle at that instant are

a)		$\frac{h}{3}$ $\sqrt{\frac{2 gh}{3}}$
b)		$\frac{h}{3}$ ,2 $\sqrt{\frac{gh}{3}}$
c)		$\frac{2 h}{3} \sqrt{\frac{2 gh}{3}}$
d)		$\frac{h}{3} \sqrt{2 gh}$

2. A ball whose K.E is E is projected at an angle of $45^{0}$ to the horizontal. The K.E of the ball at the heighest point of its flight will be

a)		E
b)		E/ $\sqrt{2}$
c)		E/2
d)		zero

3. A ball of mass m moving with velocity V collides with an identical ball at rest. After collision, the Ist ball comes to rest. The speed of the other ball is

a)		V
b)		V/2
c)		2V
d)		0

4. If the momentom of a body increases by 0.01% then its K.E will increases by

a)		0.01%
b)		0.02%
c)		0.04%
d)		0.08%

5. A rod elongates by l when a body of mass M is suspended from it. The workdone is

a)		Mgl
b)		1/2Mgl
c)		2Mgl
d)		zero

6. In a gravitational field, the workdone in transporting mass from one point to another depends on.

a)		end positions
b)		distance between them
c)		actual path of motion
d)		velocity of transport

7. If water falls from a dam into a turbine wheel 19.6m below. Then velocity of water at turbine is

a)		9.8 m/s
b)		19.6 m/s
c)		39.2 m/s
d)		98 m/s

8. Which of the following is not a perfectly in elastic collision.

a)		striking of two glass balls
b)		a ballet striking a bag of sand
c)		An $\bar{e}$ captured by a proton
d)		A man jumping onto a moving cart

9. A car is moving with a speed of 40 km/h can be stopped by applying brakes after at least 2m. If the same car is moving with speed of 80 km/h. Whats the minimum stopping distance.

a)		8m
b)		6m
c)		4m
d)		2m

10. A force (m $v^{2} / r)$ is acting on a body of mass m moving with a velocity V in a circle of radius r. What is workdone by the force in moving the body over half the circumference of the circle

a)		$\frac{m v^{2}}{r} \times π r$
b)		zero
c)		$\frac{m v^{2}}{r^{2}}$
d)		$\frac{Π r^{2}}{m v^{2}}$

11. Consider a car moving along a straight horizontal road with a speed of 72 km/h. If the coefficient of static friction between road and tyres is 0.5, the shortest distance in which the car can be stopped is

a)		30m
b)		40m
c)		72m
d)		20m

12. If K.E of a body increases by 0.1%, The percent increase in its momentum will be

a)		0.05%
b)		0.1%
c)		1%
d)		10%

13. A ball falls from rest from a height h onto a floor, and rebounds to a height h/4. The coefficient of restitution between the ball and the floor is

a)		$\frac{1}{2}$
b)		$\frac{1}{4}$
c)		$\frac{1}{\sqrt{2}}$
d)		$\frac{3}{4}$

14. A mass $m_{1}$ moves with great velocity. It strikes another mass $m_{2}$ at rest in a head on collision. It comes back along its path with low speed, after collision

a)		$m_{1} > m_{2}$
b)		$m_{1} < m_{2}$
c)		$m_{1}$ = $m_{2}$
d)		cant say

15. The principle of conservation of linear momentum can be strictly applied during a collision between two particles provided the time of impact is

a)		extremely small
b)		moderately small
c)		extremely large
d)		depends on a particular case

16. A ballet of mass a and velocity b is fixed into a large block of mass c. The final velocity of the system is

a)		$\frac{cb}{a + b}$
b)		$\frac{ab}{a + c}$
c)		$\frac{(a + b) a}{c}$
d)		$\frac{(a + c) b}{a}$

17. What is the mass of an electron moving with velocity of 0.5 C in terms of electronic rest mass ( $m_{0})$

a)		$m_{0}$
b)		4/5 $m_{0}$
c)		5/4 $m_{0}$
d)		2m

18. When the brakes of a car going at 90km/h are locked how much farther will it skid than if the brakes lock at 30km/h?

a)		Nine time farther
b)		Three times farther
c)		Two times farther
d)		none of the above

19. A motor cysle is moving along a straight horizontal road with a speed $V_{0} .$ If the coefficient of friction between the tyres and road is $μ .$ The short distance in which the car can be stopped is

a)		$\frac{{V_{0}}^{2}}{2 Mg}$
b)		$\frac{V^{2}}{μ}$
c)		$(\frac{V_{0}}{Mg})^{2}$
d)		$\frac{V_{0}}{Mg}$

20. A motor of 100HP moves with a uniform peed of 72km/hr. The forward thrust applied by the engine on the car is

a)		1111N
b)		3550N
c)		2222N
d)		3730N

21. Two springs have their force constants $K_{1}$ and $K_{2}$ both are stretched till their elastic energies are equal. Then ratio of stretching forces $F_{1} / F_{2}$ is equal to

a)		$K_{1} / K_{2}$
b)		$K_{2} : K_{1}$
c)		$\sqrt{K_{1}} : \sqrt{K_{2}}$
d)		${K_{2}}^{2} : {K_{1}}^{2}$

22. What is the shape of the graph between speed and K.E of a body?

a)		straight line
b)		hyperbola
c)		parabola
d)		exponential

23. If two protons are brought near one another, the P.E of the system will

a)		increases
b)		decreases
c)		remains the same
d)		equal to K.E

24. The vessel A and B of equal volume and weight are immersed in water to depth h. The vessel A has an oprning at the bottom through which water can enter. If the workdone is imersing A and B are $W_{A}$ and $W_{B}$ respectively then

a)		$W_{A} = W_{B}$
b)		$W_{A} < W_{B}$
c)		$W_{A} > W_{B}$
d)		$W_{A} \underset{<}{>} W_{B}$

25. The slope of potential energy versus position graph represent

a)		force
b)		work
c)		power
d)		momentum

26. A car drives along straight level frictionless road by an engine delivering constant power.Then velocity is directly proportional to

a)		t
b)		$\frac{1}{\sqrt{t}}$
c)		$\sqrt{t}$
d)		none of these

27. A particle of mass m moving towards the east with speed v collides with another particle of same mass and same speed v moving towards north.If two particles stick to each other, the new particle of mass 2m will have a speed of

a)		v
b)		v/2
c)		v/ $\sqrt{2}$
d)		v $\sqrt{2}$

28. A ball is dropped from a height h.If the coefficient of restitution be e,then to what height will it rise after jumping twice from the ground?

a)		eh/2
b)		2eh
c)		eh
d)		$e^{4} / h$

29. A particle of mass m is moving in a horizontal circle of radius r under the centripetal force= $\frac{K}{r^{2},}$ where K is a constant.The total energy of the particle is

a)		$\frac{K}{r}$
b)		$\frac{K}{2 r}$
c)		$- \frac{K}{r}$
d)		$- \frac{K}{2 r}$

30. The relation between U(r) and r for a diatomic molecule is given as
U(r)= $\frac{a}{r^{12}} - \frac{b}{r^{6}}$
The energy of dissociation of the molecule is given as

a)		$\frac{b^{2}}{4 a}$
b)		$\frac{4 a}{b^{2}}$
c)		$\frac{b^{2}}{4 a^{2}}$
d)		$\frac{4 a^{2}}{b^{2}}$

31. Liquid of density p flows along a horizontal pipe of uniform area of cross-section'a' with a velocity 'v' through a right-angled bend.The force which should be applied to the bend to hold it in equilibrium is

a)		ap $v^{2} / 2$
b)		ap $v^{2} / \sqrt{2}$
c)		2ap $v^{2}$
d)		$\sqrt{2}$ ap $v^{2}$

32. The vessels P and Q of equal volume and weight are immersed in water to depth h.The vessel P has an opening at the bottom through which water can enter.If the work done in immersing PLQ are $W_{P} and W_{Q}$ respectively,then

a)		$W_{P} = W_{Q}$
b)		$W_{P} > W_{Q}$
c)		$W_{P} < W_{Q}$
d)		$W_{P} \geq W_{Q}$

33. A machine, which is 75% efficient,uses 12 J of energy in lifting up a ikg mass through a crtain distance.The mass is then allowed to fall through that distance.The velocity at the end of its fall is (in m/s)

a)		$\sqrt{24}$
b)		$\sqrt{32}$
c)		$\sqrt{18}$
d)		$\sqrt{9}$

34. A particle moves under a force F=cx from x=0 to x= $x_{1} .$ The work done is equal to

a)		Zero
b)		C $x_{1}^{2}$
c)		$\frac{C x_{1}^{2}}{2}$
d)		$\frac{C x_{1}^{3}}{3}$

35. A metal ball of mass 2 kg moving with a speed of 36 km/hr has a head-on collision with a stationary ball of mass 3kg.If after collision both the balls move together,then the loss in kinetic energy due to collision is

a)		40 J
b)		60 J
c)		100 J
d)		140 J

36. Two springs A and B with spring constants, $k_{A}$ = ${2 k}_{B}$ are stretched by applying forces of equal magnitudes at their ends.If the energy stored in A is E,then the energy stored in B is

a)		E/4
b)		E/2
c)		E
d)		2E

37. If two balls, each of mass 0.06kg moving in opposite directions with a speed 4 m/s,collide and rebound with same speed,then impulse imparted to each ball due to other is

a)		0.48 kg m/s
b)		0.24 kg m/s
c)		0.81 kg m/s
d)		zero

38. A particle moves along the x-axis from x= $x_{1}$ to x= $x_{2}$ under the influence of a force given by F=2x.Work done in the progress is

a)		zero
b)		$x_{2}^{2} - x_{1}^{2}$
c)		2 $x_{2} (x_{2} - x_{1})$
d)		2 $x_{1} (x_{2} - x_{1})$

39. The KE acuired by a mass m in travelling a certain distance $d_{1}$ starting from rest,under the action of a constant force is directly proportional to

a)		m
b)		$\sqrt{m}$
c)		1/ $\sqrt{m}$
d)		independent of m

40. A body is allowed to fall on the ground from a height $h_{1} .$ If it is to rebound to a height $h_{2}$ ,then the coefficient of restitution is

a)		$h_{2} / h_{1}$
b)		$\sqrt{h_{2} / h_{1}}$
c)		$h_{1} h_{2}$
d)		$\sqrt{h_{1} h_{2}}$

41. A mass m moving horizontally with velocity $v_{0}$ strikes a pendulum of mass m.If the two masses stick together after the collision, then the maximum height reached by the pendulum is

a)		$v_{0}^{2} / 8 g$
b)		$v_{0}^{2} / 2 g$
c)		$\sqrt{{2 v}_{0} g}$
d)		$\sqrt{v_{0} g}$

42. At her maximum height, a girl in a swing is 3m above the ground and at lowest point she is 2m above the ground.What is her maximum velocity?

a)		$\sqrt{29.4}$ m/s
b)		$\sqrt{9.8}$ m/s
c)		$\sqrt{19.6}$ m/s
d)		$9.8$ m/s

43. A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration $a_{c} = K^{2} {rt}^{2}$ where K is a constant.The power delivered to the particle by the forces acting on it is

a)		zero
b)		$m K^{2} {r^{2} t}^{2}$
c)		$m K^{2} r^{2} t$
d)		$m K^{2} rt$

44. The speed v reached by a car of mass m,driven with constant power P, is given by

a)		v= $\frac{3 xP}{m}$
b)		v= ${(\frac{3 xP}{m})}^{\frac{1}{2}}$
c)		v= ${(\frac{3 xP}{m})}^{\frac{1}{3}}$
d)		v= ${(\frac{3 xP}{m})}^{2}$

45. The earth circles the sun once a year.The work which would have to be done on the earth to bring it to the rest relative to the sun is (ignore the rotation of the earth about its own axis.Given that mass of the earth = 6 $\times 10^{24} kg$ and distance between the sun and the earth is 1.5 $\times 10^{8} km)$

a)		2.7 $\times 10^{30} J$
b)		2.7 $\times 10^{31} J$
c)		-2.7 $\times 10^{33} J$
d)		2.7 $\times 10^{33} J$

46. A spring is compressed so that its stored energy is 2.4J.It ends are in contact with masses 1g and 48 g placed on a frictionless table.When the spring is released, the heavier mass will acquire a speed of

a)		$\frac{24}{49} m / s$
b)		$2.4 \frac{48}{49} m / s$
c)		$\frac{10^{3}}{7} cm / s$
d)		$\frac{10^{6}}{7} cm / s$

47. A uniform chain has mass M and length L respectively.It is lying on a smooth horizontal table with half of its length hanging vertically down.The work done in pulling the chain up the table is

a)		$\frac{MgL}{2}$
b)		$\frac{MgL}{4}$
c)		$\frac{MgL}{8}$
d)		$\frac{MgL}{16}$

48. Two bodies M and N of equal masses are suspended from two separate springs of spring constants $k_{1}$ and $k_{2}$ respectively.If the two bodies oscillate vertically such that their maximum velocities are equal,the ratio of the amplitude of vibration of M to that of N is

a)		$\frac{k_{1}}{k_{2}}$
b)		$\sqrt{\frac{k_{1}}{k_{2}}}$
c)		$\frac{k_{2}}{k_{1}}$
d)		$\sqrt{\frac{k_{2}}{k_{1}}}$

49. A ball is thrown vertically upwards with a velocity of 10m/s. It returns to the ground with a velocity of 9m/s. If g=9.8 $\frac{m}{s^{2},}$ then the maximum height attained by the ball is nearly

a)		5.1 m
b)		4.1 m
c)		4.61 m
d)		5.0 m

50. A spring iscompressed between two toy carts of masses $m_{1}$ and $m_{2} .$ When the toy carts are released, the spring exerts on each toy cart equal and opposite forces for the same time t.If the coefficients of friction $μ$ between the ground and the toy carts are equal, then the displacement of the toy carts are in the ratio

a)		$\frac{s_{1}}{s_{2}} = \frac{m_{2}}{m_{1}}$
b)		$\frac{s_{1}}{s_{2}} = \frac{m_{1}}{m_{2}}$
c)		$\frac{s_{1}}{s_{2}} = {(\frac{m_{2}}{m_{1}})}^{2}$
d)		$\frac{s_{1}}{s_{2}} = {(\frac{m_{1}}{m_{2}})}^{2}$