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Question Bank No: 2

1. A body of mass 60 kg is dragged with just enough force to start moving on a rough surface with coefficient of static and kinetic frictions are 0.5 and 0.4 respectively.On applying the same force,what is the acceleration?

a)		zero
b)		0.54 ${\frac{m}{s}}^{2}$
c)		0.98 ${\frac{m}{s}}^{2}$
d)		9.8 ${\frac{m}{s}}^{2}$

2. Two blocks A and B of masses 4kg and 3kg rest on a frictionless surface.A force of 7 N acts on A as shown in the image.The force exerted by A and B is
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a)		Zero
b)		3N
c)		4N
d)		7N

3. Kinetic energy being scalar is changed because K.E.of both bodies will increase.

a)		147 cm/s
b)		49 cm/s
c)		196 cm/s
d)		98 cm/s

4. Internal force can change

a)		Linear momentum as well as kinetic energy
b)		Linear momentum bu not the kinetic energy
c)		the kinetic energy but not linear momentum
d)		neither the linear momentum nor the kinetic energy

5. Which of the following statements about the centripetal and centrifugal forces is correct?

a)		Centripetal force is experimental by the observer at the centre of the circular path described by the body
b)		Centripetal force balances the centrifugal force
c)		Centripetal force is directed opposite to the centrifugal force
d)		Both the centripetal and centrifugal forces act on the same body simultanously

6. A force of $(\overset{\land}{i} + \overset{\land}{j}) N acts on a particle of mass 0.1 kg . If it starts from rest, its position at t = 1 s will be$

a)		$(\overset{\land}{i} + \overset{\land}{j}) m$
b)		$(\vec{i} + \overset{\land}{j}) m$
c)		$(\overset{\land}{5 i} + \overset{\land}{6 j}) m$
d)		$(\overset{\land}{5 i} + \overset{\land}{5 j}) m$

7. If E,G, and N represent the magnitude of electromagnetic, gravitational and nuclear forces between two electrons at a 1 mm separation, then

a)		N=E=G
b)		N>G>E
c)		E>G>N
d)		E<N<G

8. A machine gun fires n bullets per second and the mass of each bullet is m. If v is the speed of each bullet, then the force exerted on the machine gun is

a)		mgv
b)		mnv
c)		${mv}^{2} g$
d)		${mv}^{2} n$

9. On a stationary sail boat,air is blown at the sails from a fan attached to the boat.The boat will

a)		remain at rest
b)		spin around
c)		move in direction opposite in which air is blown
d)		move in direction opposite to that in which air is blown

10. A block of mass m, lying on a rough horizontal plane, is acted upon by a horizontal force P and another force Q is inclined at an angle $θ$ to the vertical, the block will remain in equilibrium. If the coefficient of friction between it and the surface is
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a)		(P+Q sin $θ$ )/ (mg+ Qsin $θ$ )
b)		(P cos $θ$ + Q )/(mg-Q sin $θ$ )
c)		(P + Q cos $θ$ 0/(mg+Q sin $θ$ )
d)		(P sin $θ$ -Q)/(mg-Q cos $θ$ )

11. A block slides with a velocity of 10m/s on a rough horizontal surface. It comes to rest after covering a distance of 50 metres. If g is 10 m/ $s^{2}$ , then the coefficient of dynamic friction between the block and the surface is

a)		0.1
b)		1
c)		10
d)		5

12. Frictional force increases when surfaces in contact are made very -very smooth. This is because

a)		of molecular forces
b)		of decrease in surface area
c)		of decrease in irregularities
d)		of increase in area

13. A body of mass 2 kg rests on a rough inclined plane making an angle $30^{o}$ with the horizontal. The coefficient of static friction between the block and the plane is 0.7. The frictional force is on the block is

a)		9.8 N
b)		0.7 x 9.8 x $\sqrt{3}$ N
c)		9.8 x $\sqrt{3}$ N
d)		0.7x 9.8 N

14. An object is placed on the surface of a smooth inclined plane of inclination $θ$ . It takes time t to reach the bottom. If the same object is allowed to slide down at a rough inclined place of inclination $θ$ , it takes time nt to reach the bottom where n is a number greater than 1. The coefficient of friction $μ$ is given by.

a)		$μ$ =tan $θ$ $[1 - \frac{1}{n^{2}}]$
b)		$μ$ =cot $θ$ $[1 - \frac{1}{n^{2}}]$
c)		$μ$ =tan $θ$ $\sqrt{1 - \frac{1}{n^{2}}}$
d)		$μ$ =cot $θ$ $\sqrt{1 - \frac{1}{n^{2}}}$

15. A ball of mass 150g starts moving at 20m/s and is hit by a force which acts on it for 0.1 seconds. Then, the impulsive force is

a)		75 N
b)		300 N
c)		3 N
d)		30 N

16. A force acts on 3.0g particle in such a way that the position of the particle as a function of time is given by
x=3t $-$ 4 $t^{2}$ + $t^{3}$
where x is in metres and t is in seconds. The work done during the first 4s is

a)		57mJ
b)		450mJ
c)		490mJ
d)		530mJ

17. A stone of mass m is tied to a string and is moved in a verticle cycle of radious r making n revolutions per minute. The total tension in the string when the stone is at its lowest point is

a)		mg
b)		m $({g + π nr}^{2})$
c)		m(g+nr)
d)		m $[g + (π^{2} n^{2} r) / 900]$

18. A force of 100 N needs to be applied parallel to a smooth inclined plane just to hold a body on it. The angle of inclination of the inclined plane is $30^{0}$ . How much horizontal force need to be applied to do the same?

a)		50 N
b)		87 N
c)		100 N
d)		115 N

19. The potential energy for a conservation system is given by $u = a x^{2} - 6 x$ where a and b are positive constants. The law of the force governing the system is

a)		F= constant
b)		F= 6x $- 2 a$
c)		F = 6 $- 2 ax$
d)		F = 2ax

20. Three blocks of masses 4 kg, 8 kg and 24 kg are connected to each other with light strings and placed on a smooth horizontal floor as shown in the figure , F is
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a)		36 N
b)		72 N
c)		18 N
d)		108 N

21. A fireman wants to slide down a rope. The breaking load for the rope is $\frac{3}{4}$ th of the weight of the man. With what acceleration should the fireman slide down?

a)		g/4
b)		g/2
c)		3g/4
d)		zero

22. With what minimum acceleration can a fire-man slide down a rope whose breaking strength is $\frac{2}{5}$ th of his weight ?

a)		1 g
b)		0.4 g
c)		0.6 g
d)		0.8 g

23. The potential energy of a body of mass m is given by U = ax+ by, where x and y are the position of co-ordinated of the particle. The acceleration of the particle is

a)		$\frac{a^{2} + b^{2}}{m}$
b)		$\frac{{(a + b)}^{\frac{1}{2}}}{m}$
c)		$\frac{a + b}{m}$
d)		$\frac{{(a^{2} + b^{2})}^{\frac{1}{2}}}{m}$

24. A string of length L and mas M is lying on a horizontal table. A force F is applied at one of tis ends. Tension in the string at a distance y from its end at which the force is applied is

a)		zero
b)		F
c)		$\frac{F (L - y)}{L}$
d)		$\frac{F (L - y)}{M}$

25. A block of metal weighing 2 kg is resting on a frictionless plane. It is struck by a jet releasing water at arate of 1 kg/m and at a speed of 5 m/s. The initial acceleration of the block will be

a)		2.5 $\frac{m}{s^{2}}$
b)		5 $\frac{m}{s^{2}}$
c)		10 $\frac{m}{s^{2}}$
d)		20 $\frac{m}{s^{2}}$

26. A fire man of mass 60 kg slides down a pole. He is pressing the pole with a force of 600 N. The coefficient of friction between the hands and the pole is 0.5. With what acceleration will the fireman slide down?

a)		2.5 $\frac{m}{s^{2}}$
b)		10 $\frac{m}{s^{2}}$
c)		1 $\frac{m}{s^{2}}$
d)		5 $\frac{m}{s^{2}}$

27. A block slips with constant velocity on a plane inclined at an angle $θ$ . The same block is pushed up the plane with an initial velocity u. The distance covered by the block before coming to rest is

a)		$\frac{u^{2} \sin^{2} θ}{2 g}$
b)		$\frac{u^{2}}{2 g \sin θ}$
c)		$\frac{u^{2} \sin^{2} θ}{4 g}$
d)		$\frac{u^{2}}{4 g \sin θ}$

28. A particle of mass 4 m which is at rest explodes into three fragments. Two of the fragments each of the mass m are found to move with a speed u each in mutually perpendicular directions. The total energy released in process of explosion is

a)		m $u^{2}$
b)		$\frac{3}{{2 mu}^{2}}$
c)		2m $u^{2}$
d)		3m $u^{2}$

29. A constant force acts on a body of mass m at rest. The velocity $ν$ acquired in transversing a specific distance depends on m as

a)		$ν α m$
b)		$ν α \frac{1}{m}$
c)		$ν α \sqrt{m}$
d)		$ν α \frac{1}{\sqrt{m}}$

30. A machine gun has a mass 5 kg. It fires 50 g bullets at a rate of 30 bullets per minute at a speed of 400 m/s. What force is required to keep the gun in position?

a)		5 N
b)		10 N
c)		15 N
d)		30 N

31. A chain of mass m and length L is held vertical by fixing its upper end to a rigid support. The tension in the chain at a distance x from the rigid support is

a)		mg
b)		$\frac{mg x}{L}$
c)		$\frac{mg L}{L - x}$
d)		$\frac{mg}{L} (L - x)$

32. A man drops an apple in the lift. He finds that the apple remains stationary and does not fall. The lift is

a)		going down with constant speed
b)		going up with constant speed
c)		going down with constant acceleration g
d)		going up with constant acceleration

33. A mass of 8 kg is suspended by a massless string of length 5m from a ceiling. A force of 80 N is applied in a horizontal direction at the midpoint of the string. the angle made by the string with the vertical in equilibrium condition will be

a)		$30^{0}$
b)		$45^{0}$
c)		$60^{0}$
d)		$90^{0}$

34. A body of mass m has its position x at a time t expresssed by the equation
x = 3 $t^{\frac{3}{2}} + 2 t^{\frac{- 1}{2}}$
The instantaneous force on the body is proportional to

a)		t
b)		$t^{0}$
c)		$t^{\frac{3}{2}}$
d)		$t^{\frac{- 1}{2}}$

35. Three bodies A, B and C have masses of 1 kg, 2 kg and 3 kg respectively. If all the bodies have equal kinetic energy, then which body has a greater momentum?

a)		Body A
b)		Body B
c)		Body C
d)		cannot be predicted

36. Two masses A and B of 10 kg and 5kg respectively are connected by a string passing over a frictionless pulley fixed at the edge of a table as shown in the figure. the coefficient of friction of A with the table is 0.2. The minimum mass of C taht may be placed on A to prevent it from moving is equal to
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a)		15 kg
b)		10 kg
c)		5 kg
d)		0 kg

37. A car turns a corner on a slippery road at a constant speed of ${10 ms}^{- 1}$ . If the coefficient of friction is 0.5, the minimum radius of the arc in metre in which the care turns is

a)		20
b)		10
c)		5
d)		4

38. A stationary body is slowly lowered on to a massive platform moving horizontally at a speed of 4 ${ms}^{- 1}$ . Through what distance will the body slide relative to the platform if the coefficient of friction is 0.2? (g = 10 ${ms}^{- 2}$ )

a)		16 m
b)		8 m
c)		4 m
d)		2 m

39. A 60 kg object is pushed with just enough force to start in moving across the floor and the same force continues to act afterwards. Find the acceleration of the body. Given coefficients of static and kinetic friction are 0.5 and 0.4 respectively.

a)		3.9 ${ms}^{- 2}$
b)		4.9 ${ms}^{- 2}$
c)		0.98 ${ms}^{- 2}$
d)		zero

40. Two wooden blocks A and B placed on a horizontal surface are connected by a string. Block B is pulled by a force of 12 N so that the blocks move forward with the same acceleration. If the surface is frictionless, the tension T in the string connecting the two blocks is
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a)		2 N
b)		4 N
c)		6 N
d)		12 N

41. A smooth inclined plane of length $l$ and height $h$ is inclined at an angle $θ$ with the horizontal. A body starts from rest and slides down the inclined surface. Then the time taken by it to reach the bottom is
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a)		$\sqrt{2 h g \sin θ}$
b)		$\sqrt{2 l \sin θ / g}$
c)		$(1 / \sin θ) \sqrt{2 h / g}$
d)		$\sqrt{2 l / g \sin θ}$

42. Starting from rest a body slides down a $45^{\circ}$ inclined plane in twice the time it takes to slide down the same distance in the absence of friction. The coefficient of friction between the body and the plane is

a)		0.80
b)		1/ $\sqrt{2}$
c)		25
d)		0.75

43. A weight W rests on a rough horizontal plane. If the angle of friction is $θ$ , the least force that will move the body along the plane is

a)		W cos $θ$
b)		W tan $θ$
c)		W cot $θ$
d)		W sin $θ$

44. A heavy box is thrust across a rough floor with an initial speed of 4 ${ms}^{- 1}$ . It stops moving after 8 second. If the resistance force of friction is 10 N, the mass of the box in kg is

a)		40
b)		20
c)		5
d)		2.5

45. A body of mass 1 kg sliding on a surface with an initial velocity 10 ${ms}^{- 1}$ is stopped by friction in 1 second. The force of friction is

a)		0.1 N
b)		10 N
c)		20 N
d)		1N

46. A block of mass 2 kg rests on a rough inclined plane making an angle of $30^{\circ}$ with the horizontal. The coefficient of static friction between the block and the palne is 0.7. The frictional force on the block is

a)		9.8 N
b)		0.7 $\times$ 9.8 $\sqrt{3}$ N
c)		9.8 $\sqrt{3}$ N
d)		0.7 $\times$ 9.8 N

47. A train of mass 40 ton moves along horizontal rails with a uniform speed of 100 km/h. The resistance due to friction is 10 kg f/ton. The force exerted by the engine is

a)		400 kg f
b)		10 kg f
c)		40,000 kg f
d)		4,000 kg f

48. A rope lies on a horizontal table so that part of it hangs over the edge. The rope begins to slide down when the length of the hanging part is 20% of its length. The coefficient of friction between the rope and the table is

a)		0.5
b)		0.2
c)		0.25
d)		0.8

49. A box of mass 10 kg slides down a rough inclined plane of inclination $30^{\circ}$ with uniform speed. The coefficient of friction in this case is

a)		0.5
b)		0.87
c)		0.49
d)		0.58

50. A small block B of mass m is held at rest at the upper edge A of a concave hemispherical bowl of radius R and released. What will be the normal reaction exerted by the surface on the block at the lowest position of the block?

a)		mgR
b)		2 mgR
c)		3 mg
d)		4 mgR