Untitled Document

Question Bank No: 1

1. An aeroplane is flying horizontally with a velocity of 600 km/h and at a height of 1960m. When it is vertically above a point A on the ground the bomb is released from it. The bomb strikes the ground at point B. The distance AB is

a)		1200 m
b)		0.33 km
c)		3.33 km
d)		33km

2. A string can with stand a tension 25N. What is the greatest speed at which a body of mars 1 kg can be whirled in a horizontal circle using 1m lenght of the string

a)		2.5 m/s
b)		5 m/s
c)		7.5 m/s
d)		10 m/s

3. An electric fan has blades of length 30 cm measured from the axis of rotation, If the fan is rotating at 120 rpm, the acceleration of a point on the tip of the blase is

a)		1600 m/ $s^{2}$
b)		47.4 m/ $s^{2}$
c)		23.7 m/ $s^{2}$
d)		50.55 m/ $s^{2}$

4. A body is moving with a velocity v on a horizontal surface of friction co-efficient M it will come to rest in time t is given by

a)		v/Mg
b)		2g / Mv
c)		$\frac{V}{2 Mg}$
d)		$\frac{2 V}{Mg}$

5. The ratio of angular speed of minutes hand and hour hand of a watch is

a)		6 : 1
b)		12 : 1
c)		1 : 6
d)		1 : 12

6. The path of the projectile as seen from another projectile is

a)		a parabola
b)		an ellipse
c)		a straight line
d)		a circle

7. Two balls are projected at an angle $θ$ and (90- $θ)$ to the horizontal with the same speed. The ratio of their maximum vertical height

a)		1 : 1
b)		tan $θ$ : 1
c)		1 : tan $θ$
d)		$\tan^{2} θ$ : 1

8. Given that A and B are greater than 1. The magnitude of ( $\vec{A} \times \vec{B}$ ) cannot be

a)		equal to AB
b)		less than AB
c)		more than AB
d)		equal to A/B

9. Three vectors $\vec{A}$ , $\vec{B}$ and $\vec{C}$ satisfy the relation $\vec{A} . \vec{B} = 0$ $\vec{A} . \vec{C} = 0$ if $\vec{B}$ and $\vec{C}$ are not lying in the same plane, $\vec{A}$ is parallel to

a)		$\vec{B}$
b)		$\vec{C}$
c)		$\vec{B} \times \vec{C}$
d)		$\vec{B} . \vec{C}$

10. The square of resultant of two equal forces is three times their product. Angle between the forces is

a)		$π$
b)		$π / 2$
c)		$π / 4$
d)		$π / 3$

11. A boat is moving with velocity 3 $\hat{i}$ +4 $\hat{j}$ w.r. to the ground. The water in the river is moving with velocity -3 $\hat{i} - 4 \hat{j}$ w.r. to the ground. The relative velocity of the boat w.r. to water is

a)		8 $\hat{j}$
b)		-6 $\hat{i} - 8 \hat{j}$
c)		6 $\hat{i} + 8 \hat{j}$
d)		5 $\sqrt{2}$

12. A man walks 8m towards east, 6m towards north. The magnitude of displacement is

a)		14 m
b)		2 m
c)		10 m
d)		( $8^{2} + 6^{2}$ ) m

13. Maximum and Minimum magnitudes of the resultant of two vectors of magnitudes P and Q are in the ratio 3 : 1which of the following relation is true

a)		P = Q
b)		P = 2 Q
c)		P Q = 1
d)		None of the above

14. A gramophone record is revolving with an angular velocity $ω .$ A coin is placed at a distance R from the centre of the record. The static coefficient of friction is $μ .$ The coin will revolve with the record if

a)		R= $\frac{μ_{g}}{ω^{2}} only$
b)		R $< \frac{μ_{g}}{w^{2}}$ only
c)		T'= $\sqrt{\frac{3}{2}} T$
d)		T' = $\frac{3}{2} T$

15. Certain neutron stars are believed to be rotating at about 1 rad/sec. If such a star has a radius of 20 km, the acceleration of an object on the equator of the star will be

a)		2 $\times 10^{4} m / s$
b)		120 $\times 10^{3} m / s^{2}$
c)		8 $\times 10^{5} m / s^{2}$
d)		4 $\times 10^{5} m / s^{2}$

16. What should be the angular velocity of the earth so that a body on its equator is weight less?

a)		$\frac{1}{8, 000} rad / s$
b)		$\frac{1}{8} rad / s$
c)		$\frac{1}{800} rad / s$
d)		$\frac{1}{80} rad / s$

17. A body slides down a frictionless track which ends in a circular loop of diameter D. Then the minimum height h of the body in terms of D so that it may just complete the loop

a)		h = $\frac{5}{2} D$
b)		h = $\frac{3}{2} D$
c)		h = $\frac{5}{4} D$
d)		h= 2D

18. The string of a pendulum of length l is displaced through $90^{0}$ from the vertical and released. Then the minimum strength of the string in order to withstand the tension as the pendulum passes through the mean position is

a)		2 mg
b)		6 mg
c)		3 mg
d)		5 mg

19. The maximum speed at which a car can take turn round a curve of 36 m radius on level road without skidding is (given coefficient of friction between the tyre and road is 0.4)

a)		4 m/s
b)		12 m/s
c)		15 m/s
d)		20m/s

20. The diameter of a solid disc is 0.5 m and its mass is 16 kg. What torque is required to increase its angular velocity from zero to 120 rotations/minute in 8 seconds?

a)		$\frac{π}{2} N - m$
b)		$π N - m$
c)		$\frac{π}{4} N - m$
d)		$\frac{π}{8} N - m$

21. The slope of the smooth banked horizontal road is $ρ .$ If the radius of the curvature be r. The maximum velocity with which a car can negotiate the curve is given by

a)		$ρ γ_{g}$
b)		$ρ / γ_{g}$
c)		$\sqrt{ρ γ_{g}}$
d)		$\sqrt{ρ / γ_{g}}$

22. The ratio of velocities at points A,B and C in vertical circular motion is
motiontwothreedimen-q12

a)		1:2:3
b)		1:3:5
c)		1:9:25
d)		1: $\sqrt{3} : \sqrt{5}$

23. A projectile thrown with velocity v making angle $θ$ with vertical gains maximum height H in the time for which the projectile remains in air, the time period is

a)		$\sqrt{H \cos θ / g}$
b)		$\sqrt{2 Hcos θ / g}$
c)		$\sqrt{4 H / g}$
d)		$\sqrt{8 H / g}$

24. In a projectile motion, the velocity

a)		is never perpendicular to the acceleration
b)		is always perpendicular to the acceleration
c)		is perpendicular to acceleration at one instant only
d)		is perpendicular to acceleration at two instants

25. A projectile is thrown with an initial velocity of (a $\hat{i}$ +b $\hat{j}) m / s .$ If the range of the projectile is double the maximum height reached by it

a)		a= 2b
b)		b=4a
c)		b=2a
d)		b=a

26. A plane surface is inclined making an angle $θ$ above the horizon. A bullet is fired with the point of projection at the bottom of the inclined plane with a velocity u, then the maximum range is given by

a)		$\frac{u^{2}}{g}$
b)		$\frac{u^{2}}{g (1 + \cos θ)}$
c)		$\frac{u^{2}}{g (1 + \sin θ)}$
d)		$\frac{u^{2}}{g (1 - \sin θ)}$

27. A body is projected making an acute angle with the horizonatl. If the angle between velocity $\vec{V}$ and acceleration $\vec{g}$ is $θ$ and given by

a)		$θ = 0^{0}$
b)		$θ = 90^{0}$
c)		$90^{0} < θ < 0^{0}$
d)		$0^{0} < θ < 180^{0}$

28. A projectile is projected with a kinetic energy K. Its range is R. It will have the minimum kinetic energy, after covering a horizontal distance equal to

a)		R
b)		3R/4
c)		R/4
d)		R/2

29. Two bullets are fired horizontally with different velocities from the same height. Which will reach the ground first?

a)		both will reach simultaneously
b)		Faster one
c)		Slower one
d)		It cannot be predicted

30. If $| \vec{A} \times \vec{B} | = 0 and \vec{B} . \vec{A}$ =-AB, the angle between $\vec{A}$ and $\vec{B}$ is

a)		zero
b)		$π / 4$
c)		$π / 2$
d)		$π$

31. If $| \vec{V_{1}} + \vec{V_{2}} | = | \vec{V_{1}} - \vec{V_{2}} | and | \vec{V_{2}} | is$ finitr, then

a)		$\vec{V_{1}}$ is parallel to $\vec{V_{2}}$
b)		$\vec{V_{1}}$ = $\vec{V_{2}}$
c)		$\| \vec{V_{1}} \| = \| \vec{V_{2}} \|$
d)		$\vec{V_{1}}$ and $\vec{V_{2}}$ are mutually perpendicular

32. The initial velocity of a particle is $\vec{u} = (2 \hat{i} + 3 \hat{j}) m / s$ A constant force of
$\vec{F} = (4 \hat{i}$ + $\hat{j}) N$ acts on the particle. It follows that

a)		its velocity is constant
b)		its path is a straight line
c)		it moves in a circular path
d)		its path is parabolic

33. If $\vec{A}$ =-4 $\hat{i} + 3 \hat{j} and \vec{B}$ = 2 $\hat{i}$ +5 $\hat{j}$ and $\vec{C}$ = $\vec{A} \times \vec{B}$ then the vector $\vec{C}$ makes an angle of

a)		$0^{0} with z - axis$
b)		$180^{0} with z - axis$
c)		$180^{0} with y - axis$
d)		$45^{0} with x - axis$

34. A region is specified by the potential function, $Ψ = 6 x + 7 y - 3 z,$ then the field in the region is

a)		$6 \hat{i} + 7 \hat{j} + 3 \hat{k}$
b)		$6 \hat{i} + 7 \hat{j} - 3 \hat{k}$
c)		$- 6 \hat{i} + 7 \hat{j} - 3 \hat{k}$
d)		$- 6 \hat{i} - 7 \hat{j} + 3 \hat{k}$

35. A mass of 2.9 kg is suspended from a string of length 50 cm and is at rest. Another body of mass 0.1 kg moving horizontally with a velocity of 150 m/s strikes and sticks to it. The tension in the string when it makes an angle of $60^{0}$ with the vertical is

a)		130 N
b)		140 N
c)		145 N
d)		135 N

36. The resultnat of two vectors $\vec{P}$ and $\vec{Q}$ is $\vec{R}$ . If Q is doubled the new resultant is perpendicular to P, then R equals

a)		P
b)		Q
c)		$(P - Q)$
d)		$(P + Q)$

37. A particle is describing the circular path of radius 20 m in every 2 s. The average angular speed of the particle during 4 sec is

a)		20 $π rad / s$
b)		4 $π rad / s$
c)		$π rad / s$
d)		2 $π rad / s$

38. A car is moving with speed 30 m/s on a circular path of radius 500 m. Its speed is increasing at the rate of 2 m/ $s^{2}$ . What is the acceleration of the car ?

a)		2 m/ $s^{2}$
b)		2.7 m/ $s^{2}$
c)		1.8 m/ $s^{2}$
d)		9.8 m/ $s^{2}$

39. A sphere of mass 0.2 kg is attached to an in-extensble string of length 0.5 m, whose upper end is fixed to the ceiling. The sphere is made to describe a horizontal circle of radius 0.3 m. The speed of the sphere will be

a)		2.5 m/s
b)		4.5 m/s
c)		3 m/s
d)		1.5 m/s

40. The speed of revolution of a particle going around a circle is doubled and its angular speed is halved. What happens to the centripeal acceleration ?

a)		Halved
b)		Doubled
c)		Remains unchanged
d)		Becomes 4 times

41. The necessary condition for a car to move on a circular level road without skidding is

a)		$\frac{m v^{2}}{r} \geq μ m g$
b)		$\frac{m v^{2}}{r} \leq μ m g$
c)		$\frac{m v^{2}}{r} = μ m g$
d)		$\frac{v}{r} = μ$

42. A particle covers equal distances around a circular path in equal intervals of time. It has uniform non-zero rate of change of

a)		linear velocity
b)		angular velocity
c)		angular displacement
d)		linear displacement

43. Keeping the banking angle same, to increase the maximum speed with which a vehicle can travel on the curved road by 10%, the radius of curvature of the road has to be changed from 25m to

a)		35.5 m
b)		30.25 m
c)		60.5 m
d)		42.25 m

44. The radius of the circular path of a particle is doubled, but its frequency of rotation remains unchanged. If the initial centripetal force be F, then the final value of centripetal force will be

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

45. At what angle to the horizontal should a ball be kicked to attain maximum height ?

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

46. A body is projected at an angle of $30^{0}$ to the horizontalwith kinectic energy E. the K.E at the topmost point is

a)		zero
b)		$\frac{E}{4}$
c)		$\frac{E}{2}$
d)		$\frac{3 E}{4}$

47. From a certain height, two bodies are projected horizontally with the velocities 10 m/s and 20 m/s. They hit the ground in $t_{1}$ and $t_{2}$ seconds. Then

a)		$t_{1}$ = $t_{2}$
b)		$t_{1}$ = $2 t_{2}$
c)		$t_{2}$ =2 $t_{1}$
d)		$t_{1}$ = $\sqrt{{2 t}_{2}}$

48. A shell on striking the ground burst and its fragments fly in all possible directions with speed up to 20 m/s. The time duration for which a person standing at a distance of 20 $\sqrt{3}$ m away from it is in danger?

a)		2 $\sqrt{3}$ s
b)		2 $(\sqrt{3 - 1})$ s
c)		2 s
d)		$\sqrt{3}$ s

49. A ball is projected from the ground at a apeed of 10 m/s making angle $30^{0}$ with the horizontal. Another ball is simultaneously released from a point on the verticle line along the maximum height of the projectile. Both the balls collide at the maximum height of the projectile. What was the initial height of the second ball?

a)		1.0 m
b)		2.0 m
c)		1.25 m
d)		2.5 m

50. The maximum height attained by the projectile is increased by 5%., Keeping the angle of projection constant, what is the precentage increase in the horizontal range?

a)		10%
b)		20%
c)		5%
d)		15%