Untitled Document

Question Bank No: 1

1. A constant power P is applied to a particle of mass m. The distance travelled by the particle when its velocity increases from $V_{1}$ to $V_{2}$ is

a)		$\frac{m}{3 P}$ ( $V_{2} - V_{1}$ )
b)		$\frac{m}{3 P} ({V_{2}}^{2} - {V_{1}}^{2})$
c)		$\frac{m}{3 P} ({V_{2}}^{3} - {V_{1}}^{3})$
d)		$\frac{3 P}{m} ({V_{2}}^{2} - {V_{1}}^{2})$

2. An express train moving at 30 m/s reduces its speed to 10 m/s in a distance of 240m. If the breaking force is increased by 20% in the begining, find the distance that it travels before coimg to rest

a)		338 m
b)		270 m
c)		300 m
d)		225 m

3. A body of mass m is accelerated uniformly from rest to a speed v in a time T. The instaneous power delivered to the body as a function of time is given by

a)		$\frac{1}{2} \frac{m v^{2}}{T^{2}}$ $t^{2}$
b)		$\frac{1}{2} \frac{m v^{2}}{T^{2}} t$
c)		$\frac{m v^{2}}{T^{2}}$ $t^{2}$
d)		$\frac{m v^{2}}{T^{2}} t$

4. Which of the following velocity-time graphs shows a realistic situation for a body in motion

a)
b)
c)
d)

5. The ratio of the numerical values of the average velocity and average speed of a body is always

a)		Unity
b)		Unity or less
c)		unity or more
d)		less than unity

6. If a body travels hald the distance with velocity $V_{1}$ and next half with velocity $V_{2}$ , its average velocity is given by

a)		V = $\sqrt{V_{1} \times V_{2}}$
b)		V = $\frac{V_{1} + V_{2}}{2}$
c)		V = $\frac{V_{1}}{V_{2}}$
d)		$\frac{2}{V} = \frac{1}{V_{1}} + \frac{1}{V_{2}}$

7. A body is projected vertically upward with a velocity u returns to the starting point in 4 sec. If g=10 m/s the value of u in m/s is

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

8. Two trains each 50m long are travelling in opposite direction with velocity 10mts abs 15 m/s. The time of crossing is

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

9. The co-ordinates of a moving particle are x = a $t^{2}$ and y =b $t^{2}$ where a and b are constants. The velocity of the particle at any moment is

a)		2t $\sqrt{a^{2} + b^{2}}$
b)		2t $\sqrt{a + b}$
c)		2t $\sqrt{a^{2} - b^{2}}$
d)		2 $\sqrt{a^{2} + b^{2}}$

10. Which one out of the following four statement is false

a)		A body can have zero velocity and still be accelerated
b)		A body can have constant velocity and still have varying speed
c)		A body can have constant speed and still have a varuing velocity
d)		The direction of the velocity of a body can change when its acceleration is constant

11. A particle moves uniformly with speed $ν$ along the parabolic path y = k $x^{2}$ , taking k as a positive constant. The direction of particle at x=0 is given by

a)		2k $v^{2}$
b)		k $v^{2}$
c)		k $v^{2} / 2$
d)		2kv

12. The displacement of a particle is proportional to the cube of time. then magnitude of this acceleration

a)		increase with time
b)		decrease with time
c)		constant but not zero
d)		zero

13. A car accelerated from rest at a constant rate $α$ for some time after which it decelerates at a constant rate $β$ to come to rest. If the total time elapsed is t, the distance travelled by a car is

a)		$\frac{1}{2} (\frac{α β}{α + β})$ $t^{2}$
b)		$\frac{1}{2} (\frac{α + β}{α β})$ $t^{2}$
c)		$\frac{1}{2} (\frac{α^{2} + β^{2}}{α β})$ $t^{2}$
d)		$\frac{1}{2} (\frac{α^{2} - β^{2}}{α β})$ $t^{2}$

14. Two bodies of different masses $m_{a}$ and $m_{b}$ are dropped from two different height a and b. The ratio of the velocity of the two to drop throufh these distances is

a)		a : b
b)		$\frac{ma}{mb}$ : b/a
c)		$\sqrt{a}$ : $\sqrt{b}$
d)		$a^{2} : b^{2}$

15. A particle moves along x axis in such a way that its x- co-ordinates varies with time t according to the equation x = (8-4t+6 $t^{2}$ ) metre. The velocity of the particle will vary with time according to the graph

a)
b)
c)
d)

16. A mass m slips along the wall of semi spherical surface of radius R. The velocity at the bottom of the surface
motionslq6

a)		$\sqrt{Rg}$
b)		$\sqrt{2 Rg}$
c)		2 $\sqrt{π Rg}$
d)		$\sqrt{π Rg}$

17. Tripling the speed of a motor car multiplies the distance needed for stopping it by

a)		3
b)		6
c)		9
d)		some other number

18. A stone is dropped into a well in which the level of water is h meter below the top of the well. If $ν$ is the velocity of sound, the time T after which the splash is heared is given by

a)		T = 2h / $ν$
b)		T = $\sqrt{\frac{2 h}{g}}$ + $\frac{h}{ν}$
c)		T = $\sqrt{\frac{2 h}{υ}}$ + $\frac{h}{g}$
d)		T= $\sqrt{\frac{h}{2 g}}$ + $\frac{2 h}{ν}$

19. An insect crawls a distance of 4m along north in 10 s and then a distance of 3m along east in 5 sec. The average velocity of the insect is

a)		7/15 m/sec
b)		1/5 m/sec
c)		5/15 m/sec
d)		12/15 m/sec

20. Which of the following time-displacement graph is not possible in nature.

a)
b)
c)
d)

21. The displacement - time graph for two particles A and B are straight line inclined at angle of $30^{\circ}$ and $60^{\circ}$ with the time axis. The ratio of velocities of $V_{A} : V_{B}$ is

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

22. Two particles, one with constant velocity 50 m/s and the other with uniform acceleration 10 m/ $s^{2},$ start moving simultaneously from the same place in the same direction.They will be at a distance of 125 m from each other after

a)		5 sec
b)		5 $(1 + \sqrt{2}) \sec$
c)		10 sec
d)		10 $(\sqrt{2} + 1) \sec$

23. A boat can go across a lake and return in time $T_{0} at a speed v . On a rough day, there is uniform current at speed v^{t} to help the onward journey and impede the return journey$ . If the time taken to go across and return on the rough day beT, then T/ $T_{0} =$

a)		1+ $\frac{v^{2}}{v^{2}}$
b)		$\frac{1}{{1 + v}^{t 2} / v^{2}}$
c)		1- $\frac{v^{2}}{v^{2}}$
d)		1+ $\frac{v^{2}}{v^{2}}$

24. The location of a particle has changed.What can we say about the displacement and the distance convered by the particle?

a)		both cannot be zero
b)		one of the two may be zero
c)		both must be zero
d)		if one is positive the other is negative and vice-versa

25. A person standing on an escalator takes time $t_{1} to reach the top of a tower when the escalator is moving . He takes time t_{2} to reach the top of the tower when the escalator is standing . How long will bhe take if he walks up a moving escalator ?$

a)		$t_{2} - t_{1}$
b)		$t_{1} - t_{2}$
c)		$\frac{t_{1} t_{2}}{t_{1} - t_{2}}$
d)		$\frac{t_{1} t_{2}}{t_{1} + t_{2}}$

26. The accelaration of a particle varies with time as a=bt+c, where b and c are constant.What will be the velocity of the particle which starts from rest after the timet?

a)		bt+ $\frac{1}{2} {cr}^{2}$
b)		ct+ $\frac{1}{2} {br}^{2}$
c)		bt+ ${cr}^{2}$
d)		ct+ ${br}^{2}$

27. A car starts from rest and acccelerates at uniform rate of 5m/ $s^{2} for some time, then moves with the constant speed for some time and retards at the same uniform rate and comes to rest . Total time for the journey is 25 \sec and average speed for the journey is 20 m / s . How long does the car move with constant speed ?$

a)		10 sec
b)		12 sec
c)		15 sec
d)		18 sec

28. Two masses M and m,situated at infinite distance apart,are at rest.Due to mutual interaction, they start approaching each other.The relative velocity of the system when the distance between them is r, will be

a)		$\frac{2 Gr}{M + m}$
b)		$\frac{2 G (M + m)}{r}$
c)		$\sqrt{\frac{2 Gr}{M + m}}$
d)		$\sqrt{\frac{2 G (M + m)}{r}}$

29. A swimmer can swim in still water with speed v and the river flowing with velocity $\frac{v}{2} . To cross the river in shortest time, he should swim making angle 0 with the upstream . What is the ratio of the time taken to swim across in the shortest time, to that in swimming across over the shortest distance ?$

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

30. A particle moving in a straight line covers half the distance with speed of 3 m/s. The other half of distance is covered in two equal time intervals with speed of 4.5 m/s and 7.5 m/s respectively.The average speed of the particle during this motion is

a)		4.0 m/s
b)		5.0 m/s
c)		5.5 m/s
d)		4.8 m/s

31. The acceleration of a particle is increasing linearly with time t and bt. The particle starts from the origin with an initial velocity $v_{0} . The distance travelled by the particle in time t will be$

a)		$v_{0} t + \frac{1}{3} {bt}^{2}$
b)		$v_{0} t + \frac{1}{3} {bt}^{3}$
c)		$v_{0} t + \frac{1}{6} {bt}^{3}$
d)		$v_{0} t + \frac{1}{2} {bt}^{2}$

32. A point moves with uniform acceleration and $v_{1}, v_{2}, v_{3} denote the average velocities in the three successive intervals of time t_{1}, t_{2} and$
$t_{3} . Which of the following relations is correct ?$

a)		${(v}_{1} - v_{2}) : {(v}_{2} - v_{3}) = {(t}_{1} - t_{2}) : {(t}_{2} + t_{3})$
b)		${(v}_{1} - v_{2}) : {(v}_{2} - v_{3}) = {(t}_{1} + t_{2}) : {(t}_{2} + t_{3})$
c)		${(v}_{1} - v_{2}) : {(v}_{2} - v_{3}) = {(t}_{1} - t_{2}) : {(t}_{1} - t_{3})$
d)		${(v}_{1} - v_{2}) : {(v}_{2} - v_{3}) = {(t}_{1} - t_{2}) : {(t}_{2} - t_{3})$

33. Two cars A and B are travelling in the same direction with velocities $v_{A} and v_{B}$
$(v_{A} > v_{B})$
When the car A is at a distance s behind the car B,the driver of the car applies the brakes producing a uniform retardation a; there will be no collision when

a)		s< $\frac{{(v_{A} - v_{B})}^{2}}{2 a}$
b)		s= $\frac{{(v_{A} - v_{B})}^{2}}{2 a}$
c)		s $\geq$ $\frac{{(v_{A} - v_{B})}^{2}}{2 a}$
d)		s $\leq$ $\frac{{(v_{A} - v_{B})}^{2}}{2 a}$

34. Train S is moving towards north with a speed of 25 m/s.A monkey is moving with a speed of 5 m/s on the roof of the train A against its motion.The speed of the monkey as seen by the observer on the ground will be.

a)		30 m/s towards north
b)		30 m/s towards south
c)		200 m/s towards north
d)		20 m/s towards south

35. A wheel of radius R rolls forward half a revolution. Then the displacement of a point of the wheel intially in contact with the ground is

a)		$π R$
b)		2R
c)		$π (R + 2)$
d)		R $\sqrt{π^{2} + 4}$

36. A ball moving horizontally towards the left with speed 5 m/s rebounds of a vertical wall which is moving towards right with speed 5 m/s. After rebounding, the speed of the ball relative to the ground will be

a)		5 m/s
b)		10 m/s
c)		15 m/s
d)		20 m/s

37. A bird flies with a speed v= $| t - 2 | m / s along a straight line, where t is time in seconds . Distance travelled by the bird during the first four seconds is equal to$

a)		2 m
b)		4 m
c)		0 m
d)		8 m

38. Rain is falling vertically downwards with a velocity of 3 km/h. A main walks in the rain with a velocity of 4km/h.The raindrops will fall on the man with a velocity of

a)		1 km/h
b)		3 km/h
c)		4 km/h
d)		5 km/h

39. A particle starts from the origin with a velocity of 10m/s and moves with a constant acceleration till the velocity increase to 50m/s.At that instant,the acceleration is suddenly reversed.What will be the velocity of the particle,when it returns to the sttarting point?

a)		Zero
b)		-10 m/s
c)		-50 m/s
d)		-70 m/s

40. A thief is running away on a straight road in a jeep moving witha speed of 9m/s.A police man chases him on a motorcycle moving at a speed of 10m/s.If the instantaneous separation of the jeep from the motorcycle is 100m, how long will it take for the policemen to catch the 'thief'?

a)		1 s
b)		90 s
c)		19 s
d)		100 s

41. A man walks in train with a velocity of 5km/hour.The raindrops strike at him at an angle of $45^{0} with the horizontal . The downward velocity of the raindrops will be$

a)		5 km/h
b)		4 km/h
c)		3 km/h
d)		1 km/h

42. The velocity-time graph of a body is shown in Figure. It implies that at BC region
motiononedimen-q6

a)		the force is zero
b)		there is a force towards motion
c)		there is a force which opposes motion
d)		there is only gravitational force

43. Figure shows that the velocity-time graph of the two particles $P_{1} and P_{2} . Which of the following statements about their relative motion is true ? Their relative velocity$
motiononedimen-q5

a)		is zero
b)		is non-zero but constant
c)		continuously decreases
d)		continuously increases

44. The velocity v versus t graph of a body in a straight line is shown in Figure.The displacement of the body in five seconds is
motiononedimen-q4

a)		2m
b)		3m
c)		4m
d)		5m

45. The area of the acceleration displacements curve of a body gives.

a)		impulse
b)		change in momentum per unit mass
c)		change in KE per unit mass
d)		total change in energy

46. The slope of velocity-time graph, for motion with uniform velocity is equal to

a)		initial velocity
b)		final velocity
c)		zero
d)		none of these

47. The time elapsed is plotted along the x-axis and the acceleration is plotted along the y-axis.The area between the graph and the x-axis gives

a)		average velocity
b)		distance covered
c)		difference in velocities
d)		difference in accelerations

48. The position vector of a particle is given by $\vec{r} = \vec{r_{0}} (1 - α t) t$ , where t is the time and $α$ and $\vec{r_{0}}$ are constants. After what time the particle returns to the starting point?

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

49. The displacement x and time t are related as $t = p x^{2} + qx + r$ , where p, q and r are constants. What is the relation between velocity v and the acceleration a?

a)		a $α v$
b)		$a^{2} α v$
c)		a $α v^{3}$
d)		$a^{2} α v^{3}$

50. A steamer takes 12 days to reach from port x to port y. Everyday only one steamer sets out from both the ports. How many steamers does each steamer meet in the open sea?

a)		23
b)		25
c)		27
d)		21