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Question Bank No: 3

1. A body of mass 1 kg moving eastward with a uniform speed of ${2 ms}^{- 1}$ has a force 2 N applied to it in the northward direction. Two second after the force is applied, the distance travelled by the body is

a)		4m
b)		8m
c)		4 $\sqrt{2}$ m
d)		6m

2. A uniform thick string of length 5m is resting on a frictionless surface in horizontal position. It is pulled by a horizontal force of 5 N from one end. The tension in the string 1 m from the end where the force is applied is

a)		zero
b)		5 N
c)		4 N
d)		1 N

3. A man standing on a lift holds a spring balance with a load of 10 kg suspended from it. The reading of the balance when the lift is descending with acceleration of 1.8 ${ms}^{- 2}$ is

a)		98 N
b)		80 N
c)		zero
d)		116 N

4. Two masses 10 kg and 20 kg respectively are connected by a massless string as shown in the fig. A force of 100 N acts on 20 kg mass. At the instant shown, the 10kg mass has an acceleration of 6 ${ms}^{- 2}$ . What is the acceleration of 20kg mass?
phlaw25

a)		12 ${ms}^{- 2}$
b)		4 ${ms}^{- 2}$
c)		2 ${ms}^{- 2}$
d)		6 ${ms}^{- 2}$

5. A string passes over two pulleys and the ends of the string are attached to masses $m_{1}$ and $m_{2} (m_{1} = m_{2})$ . At the centre of the string between the pulleys another mass m is hung in order that there is no sag in the string. The masses attached at the ends should be,

a)		2 m
b)		4 m
c)		3 m
d)		1 m

6. A body of mass 2 kg covers in successive seconds the distance of 8, 9 and 10 m respectively. The force acting on it is

a)		2N
b)		16N
c)		20N
d)		10N

7. A force of 100 N acts on a body for 5 seconds and the body acquires a velocity 30 ${ms}^{- 1}$ . The mass of the body is

a)		10 kg
b)		3.33 kg
c)		6.66 kg
d)		16.66 kg

8. Let a shot of mass 0.5 kg be fired from a gun of mass 30 kg with a speed of 180 ${ms}^{- 1}$ relative to the gun. The speed of recoil of the gun in ${ms}^{- 1}$ will be

a)		3
b)		6
c)		6.1
d)		3.05

9. If an elevator is moving vertically up with an acceleration a, the force exerted on the floor by a passenger of mass M is

a)		Ma
b)		Mg
c)		zero
d)		M (g + a)

10. A car travelling at a speed of 30 $km / hr$ is brought to a halt in 8 m by applying brakes. If the same car is travelling at 60 km/hr it can be brought to a halt with the same braking power in

a)		8m
b)		16 m
c)		24 m
d)		32m

11. In the figure three bodies of mass m, 3m, 5m are connected with strings as shown. They are pulled by a horizontal force F on a frictionless table . If $T_{1} = 16 N$ , the acceleration of the system is
phlaw18

a)		$\frac{2}{m}$
b)		$\frac{3}{m}$
c)		$\frac{9}{m}$
d)		$\frac{4}{m}$

12. Three equal weights A, B, and C of mass 2kg each are hanging on a string passing over a smooth frictionless pulley as shown. The tension in the string connecting B and C is
phlaw17

a)		zero
b)		13 N
c)		3.3 N
d)		19.6 N

13. A ball of mass 5kg is suspended from a spring balance mounted vertically in a lift. If the lift moves with constant velocity 2 ${ms}^{- 1}$ , the spring balance will read

a)		2.5 kg
b)		5 kg
c)		zero
d)		10 kg

14. A body of mass 2kg has initial velocity 3 ${ms}^{- 1}$ along OA. It is subjected to a force of 4N in a direction perpendicular to OA. The distance of the body from O after 4 second will be

a)		20 m
b)		48 m
c)		12m
d)		28m

15. A body is accelerated by applying a force of 30 N. The momentum of the body after two second in kg ${ms}^{- 1}$ is

a)		7.5
b)		30
c)		120
d)		60

16. A 2,000 kg truck travelling at 36 $\frac{km}{hr}$ strikes a tree and comes to rest in 0.1 second. The average force on the truck during the clash is

a)		$2 \times 10^{5} N$
b)		$2 \times 10^{4} N$
c)		$10^{3} N$
d)		$20 N$

17. A player catches a cricket ball of mass 150g moving at the rate of 20 ${ms}^{- 1}$ . If the catching process is completed in 0.1 second , the force of the blow exerted by the ball on the hand is

a)		3,000 N
b)		3 N
c)		30 N
d)		30,000 N

18. A rope of length L is resting on a smooth horizontal surface. It is pulled by a constant force F at one end. The tension in the rope at a distance $l$ from the end where the force applied is

a)		$\frac{FL}{l}$
b)		$\frac{F (L - l)}{L}$
c)		$FL (L - l)$
d)		$FI (L - l)$

19. Two blocks of masses 2.9 kg and 1.9 kg are suspended from a rigid support by two inextensible wires each of length 1m. The upper wire has negligible mass and the lower wire has a uniform mass of 0.2 $\frac{kg}{m}$ . The whole system of blocks have an upward acceleration of 0.2 ${ms}^{- 2} (g = 9.8 {ms}^{- 2}$ ). The tension at middle point of the lower wire is
phlaw9

a)		20 N
b)		30 N
c)		40 N
d)		50 N

20. Two blocks of masses 2.9 kg and 1.9 kg are suspended from a rigid support by two inextensible wires each of length 1m. The upper wire has negligible mass and the lower wire has a uniform mass of 0.2 $\frac{kg}{m}$ . The whole system of blocks have an upward acceleration of 0.2 ${ms}^{- 2} (g = 9.8 {ms}^{- 2}$ ). The tension at middle point of upper wire is
phlaw9

a)		20 N
b)		30 N
c)		40 N
d)		50 N

21. A bullet hits and gets embedded in a solid block resting on a horizontal frictionless table. What is conserved ?

a)		Momentum and KE
b)		KE alone
c)		PE alone
d)		Momentum alone

22. A rocket expels gas at the rate of 0.05 kg $s^{- 1}$ . If the force produced by the rocket is 100 N, the velocity with which the gas is expelled is

a)		20 ${ms}^{- 1}$
b)		200 ${ms}^{- 1}$
c)		100 ${ms}^{- 1}$
d)		2000 ${ms}^{- 1}$

23. The ratio of the gravitational force and the electrostatic force between two protons seperated by one fermi is about

a)		$10^{38}$
b)		$10^{- 38}$
c)		$10^{15}$
d)		$10^{- 15}$

24. A cricket ball of mass 50 g strikes a bat with velocity 100 ${ms}^{- 1}$ and rebounds with the same velocity within 0.01 second. The force exerted on the ball is

a)		100 N
b)		1000 N
c)		10 N
d)		500 N

25. A body of mass 10 kg is thrown vertically upwards with a velocity 20 ${ms}^{- 1}$ . Its momentum after 1 second (g = 10 ${ms}^{- 2}$ ) in kg ${ms}^{- 1}$ is

a)		200
b)		100
c)		50
d)		zero

26. A bullet of mass m is fired into a large block of wood of mass M with velocity v. The final velocity of the system is

a)		( $\frac{v}{M + m}$ )
b)		( $M + m$ ) $\frac{v}{m}$
c)		( $\frac{mv}{M}$ )
d)		$\frac{mv}{(M + m)}$

27. A body of mass $m_{1}$ moving with uniform velocity of 40 ${ms}^{- 1}$ collides with another mass $m_{2}$ at rest and then the two together move with uniform velocity 30 ${ms}^{- 1}$ . The ratio of the masses $\frac{m_{1}}{m_{2}}$ is

a)		0.75
b)		4.0
c)		1.33
d)		3

28. A ball of mass 0.05 kg hits hard vertically on the ground with a speed of 10 ${ms}^{- 1}$ . The ball is in contact with the ground for $10^{- 3}$ second and the average vertical force exerted by the ground on the ball is 1000N. The ball will rebound vertically upward with a speed

a)		30 ${ms}^{- 1}$
b)		1 ${ms}^{- 1}$
c)		zero
d)		10 ${ms}^{- 1}$

29. A body of mass $m_{1}$ moving with a uniform velocity of 40m/s collides with another mass $m_{2}$ at rest and then the too together begin to move with a uniform velocity 30 m/s. The ratio of their masses $(m_{1} / m_{2})$ is

a)		3
b)		4
c)		2
d)		1

30. Which of the following is a scalar quantity?

a)		Electric current
b)		Electric field
c)		Acceleration
d)		Linear momentum

31. The velocity of freely falling body varies according to $g^{p} h^{q}$ where 'g' is the acceleration due to gravity and 'h' is the height from where it is released. The value of p and q are

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

32. At the top of the trajectory of a projectile, the directions of velocity and acceleration are

a)		perpendicular to each other
b)		parallel to each other
c)		at an angle $45^{0}$
d)		at an angle $180^{0}$

33. While measuring the acceleration due to gravity by simple pendulum, a student makes a positive error of 1% in the length of the pendulum and a negative error of 3% in the value of time period. The percentage error in the measure measurement of 'g' is

a)		2%
b)		4%
c)		5%
d)		7%

34. If the unit of length and force be accelerated 4 times, the unit of energy is increased by

a)		4 times
b)		8 times
c)		16 times
d)		32 times

35. The engine of a jet craft applies a thrust force of $10^{5} N$ during take off and causes the plane to attain a velocity 1Km/sec in 10 seconds. The mass of plane is

a)		$10^{2} kg$
b)		$10^{3} kg$
c)		$10^{4} kg$
d)		$10^{5} kg$

36. If $X = \frac{a}{b}$ and $Δ a$ and $Δ b$ are the errors in the measurement of a and b respectively, then the maximum percentage error in the value of x will be

a)		$[\frac{Δ a}{a} + \frac{Δ b}{b}] \times 100$
b)		$[\frac{Δ a}{a} - \frac{Δ b}{b}] \times 100$
c)		$[\frac{Δ a}{a - b} + \frac{Δ b}{a - b}] \times 100$
d)		$[\frac{Δ a}{a - b} - \frac{Δ b}{a - b}] \times 100$

37. A car covers the first half of a certain distance with a speed of $v_{1}$ and the second half with a speed $v_{2} .$ The average speed during the whole journey is

a)		$\frac{v_{1} + v_{2}}{2}$
b)		$\frac{v_{1} v_{2}}{v_{1} + v_{2}}$
c)		$\frac{\sqrt{{v_{1}}^{2} + {v_{2}}^{2}}}{2}$
d)		$\frac{2 v_{1} v_{2}}{v_{1} + v_{2}}$

38. Tripling the speed of a vehicle multiplies the minimum distance needed for stopping it by

a)		3
b)		6
c)		9
d)		$\frac{9}{2}$

39. A stone dropped from the top of travels 25m in the last second of its journey. The height of the is ( $g = 10 m / s^{2})$

a)		45m
b)		90m
c)		72m
d)		135m

40. A particle starting from rest has velocity that increases linearly with time as v=kt. Then the distance covered by it in the first 3s is

a)		3k/2
b)		3k
c)		6k
d)		$\frac{9}{2} k$

41. A body is projected vertically upwards. If $t_{1}$ and $t_{2}$ be the times at which it is at height h above the point of projection while ascending and descending respectively then h is

a)		${gt}_{1} t_{2}$
b)		$\frac{1}{2} {gt}_{1} t_{2}$
c)		$2 {gt}_{1} t_{2}$
d)		$\frac{g}{t_{1} t_{2}}$

42. The displacement time graphs for two particles A and B are straight lines inclined at $30^{0}$ and $60^{0}$ to the time axis. The ratio of their speeds $ν A : ν B$ is

a)		3:1
b)		1:3
c)		$\sqrt{3} : 1$
d)		1: $\sqrt{3}$

43. A bullet fired into a fixed wooden block loses half its velocity after penetrating 60cm. It comes to rest after a further distance of

a)		10cm
b)		20cm
c)		40cm
d)		60cm

44. A balloon rises from rest with a constant acceleration g/8. A stone is released from it when it has risen to a height h. The time taken by the stone to reach the ground is

a)		$\sqrt{h / 8}$
b)		$\sqrt{2 h / 8}$
c)		$2 \sqrt{h / 8}$
d)		$4 \sqrt{h / 8}$

45. The displacement of x of a body varies with time as $x = \frac{1}{3} t^{2} + 16 t + 3$ . The time taken by the body to come to rest is

a)		36s
b)		30s
c)		26s
d)		24s

46. Starting from rest and moving with a constant acceleration a body covers a certain distance in time t. It covers the second half of the distance in time

a)		$\frac{t}{\sqrt{2}}$
b)		$\frac{t}{\sqrt{3}}$
c)		$\frac{t}{\sqrt{5}}$
d)		$t [\frac{1 - 1}{\sqrt{2}}]$

47. A stone dropped from a certain height can reach the ground in 5s. If it is stopped after 3 seconds of its fall and then allowed to fall again, the time taken by the stone to reach the ground for the remaining distance is

a)		2s
b)		3s
c)		4s
d)		6s

48. A stone thrown vertically upwards from the top of a tower with an initial velocity u reaches the ground with a velocity 3u. The height of the tower is

a)		$\frac{3 u^{2}}{8}$
b)		$\frac{4 u^{2}}{8}$
c)		$\frac{6 u^{2}}{8}$
d)		$\frac{9 u^{2}}{8}$

49. A particle projected horizontally from the top of a table touches the ground at a distance d from the bottom edge of the table. If h is the height of the table, then the velocity of projection is

a)		$\frac{h \sqrt{2 g}}{d}$
b)		$\frac{h \sqrt{g}}{2 d}$
c)		$\frac{d \sqrt{2 g}}{h}$
d)		$\frac{d \sqrt{g}}{2 h}$

50. A particle is thrown horizontally from the top of a tower of height h with a velocity $\sqrt{2 gh} .$ It it strikes the ground at a distance from the foot of the tower equals to

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