Untitled Document

Question Bank No: 1

1. An annular ring with inner and outer radii $R_{1}$ and $R_{2}$ is rolling without slipping with a uniform angular speed.The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring $F_{1} / F_{2}$ is

a)		$R_{1} / R_{2}$
b)		1
c)		${(\frac{R_{1}}{R_{2}})}^{2}$
d)		$(\frac{R_{1}}{R_{2}})$

2. Moment of couple is called

a)		Impulse
b)		Couple
c)		Torque
d)		Angular momentum

3. A particle performing uniform circular motion has angular momentum L.If its angular frequency is doubled, and its K.E halved, then the new angular momentum is

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

4. The acceleration of a solid cylinder rolling down an inclined plane of inclination $30^{0}$ is

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

5. A child swinging on a swing in sitting position stands up. The time period of the swing will

a)		Increase
b)		decrease
c)		remains same
d)		increase if the child is long and decrease if the child is short

6. The angular speed of fly wheel making 120 rpm is

a)		2 $π$ rad/s
b)		$π$ rad/s
c)		4 $π$ rad/s
d)		2 $π^{2}$ rad/s

7. A planet is moving around the sun in an elliptical orbit, its speed is

a)		The same at all points of the orbit
b)		maximum when it is nearest to sun
c)		maximum when it is farthest from the sun
d)		cannot say

8. A constant torque of 31.4 Nm is exerted on a pivoted wheel.If angular acceleration of wheel is 4 $π$ rad / $5^{2}$ .Then the moment of inertia of the wheel is

a)		2.5 kg- $m^{2}$
b)		3.5 kg- $m^{2}$
c)		4.5 kg- $m^{2}$
d)		5.5 kg- $m^{2}$

9. Which of the following qualities plays some role in rotational dynamics as OS played by mass in linear dynamics.

a)		moment of inertia
b)		toroque
c)		angular velocity
d)		none of these

10. In a uniform circular motion of a ball tied with a string,velocity at any time is at an angle Q with acceleration ,then Q is

a)		$60^{0}$
b)		$30^{0}$
c)		$90^{0}$
d)		None of these

11. A person standing on rotating platform has his hands towered. He suddenly out stretches his arms.The angular momentum

a)		becomes Zero
b)		increases
c)		decreases
d)		remains same

12. The least coefficient of friction for an inclined plane inclined at angle $\propto$ with horizontal in order that a solid cylinder will roll down it with out slipping is

a)		$\frac{2}{3} \tan \propto$
b)		$\frac{2}{7} \tan \propto$
c)		$\frac{1}{3} \tan \propto$
d)		$\frac{5}{7} \tan \propto$

13. A man is sitting with folded hands on a revolving table.Suddenly he stretches his arms angular speed of table would

a)		increase
b)		decrease
c)		remain the same
d)		nothing can be said

14. A ring and a disc have the same mass and radius.The ratio of their moment of inertia about their axis is

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

15. Of the two eggs which have identical sizes,shapes and weights, one is raw and other is half boiled.The ratio between the moment of inertia of the raw to the half boiled egg about central axis

a)		one
b)		greater than one
c)		less than one
d)		not comparable

16. The ratio of the angular velocities of hour hand and minute hand of a watch is

a)		1:1
b)		43200:1
c)		1:12
d)		1:24

17. A ring starts from rest and acquires an angular speed of 10 rad/s in 2S.The mass of the ring is 500 g and its radius is 20 cm. The torque on the ring is

a)		0.02Nm
b)		0.01Nm
c)		0.2Nm
d)		0.1Nm

18. If earth were to shrink to half its present diameter without any change in its mass,the duration of the day will be

a)		48h
b)		6h
c)		12h
d)		24h

19. A boy comes and sits suddenly on a circular rotating table.What will remain conserved

a)		angular velocity
b)		angular momentum
c)		linear momentum
d)		angular acceleration

20. A wheel starts from rest and acquires a rotational speed of 240 rps in 2 min.Its acceleration is

a)		5rp $s^{2}$
b)		2rp $s^{2}$
c)		8rp $s^{2}$
d)		11rp $s^{2}$

21. A body of mass m and radius of g y ration K rotates with angular velocity w.Angular moment of the body is

a)		mk $w^{2}$
b)		m $k^{2} w$
c)		m $k^{2} \sqrt{w}$
d)		mkw

22. If angular velocity of a body is doubled, then the ratio of its angular momentum becomes

a)		1:2
b)		1:4
c)		2:1
d)		1:8

23. A spherical solid ball of 1 kg mass and radius 3 cm is rotating about an axis passing through its centre with an angular velocity of 50 rad/s.The K.E of rotation is

a)		4500J
b)		0.45J
c)		910 J
d)		9/20J

24. One quarter of the disc of mass m is removed if r be the radius of the disc,the new M.I. is

a)		3/2 ${mr}^{2}$
b)		$\frac{{mr}^{2}}{2}$
c)		$\frac{3}{8} {mr}^{2}$
d)		none of these

25. systemofpartQ10
In a rectangle ABCD (BC=2AB).The moment of inertia is minimum along an axis through

a)		BC
b)		BD
c)		HF
d)		EG

26. The rotational K.E of a body is E and its moment of inertia is I.The angular momentum is

a)		EI
b)		$2 \sqrt{IE}$
c)		$\sqrt{2 EI}$
d)		E/I

27. For similar point masses (in each) are symmetrically placed on the circumference of a disc of mass M and radius R. MI of the system about an axis passing through centre 0 and perpendicular to the plane of the disc will be

a)		${MR}^{2} + {{}_{-}4 MR}^{2}$
b)		${MR}^{2}$ ${+ \frac{8}{5} MR}^{2}$
c)		${MR}^{2} + {4 MR}^{2}$
d)		$\frac{{MR}^{2}}{2} + {4 MR}^{2}$

28. A solid sphere of radius R has moment of inertia I about its diameter.What will be moment of inertia of a shell of some mass and some radius about its diameter?

a)		$\frac{3}{5} I$
b)		$\frac{5}{3} I$
c)		$\frac{2}{3} I$
d)		$\frac{2}{5} I$

29. When a sphere of inertia I and mass m rolls from rest down an included plane without slipping its K.E is

a)		Iw +mV
b)		0.5M $V^{2}$
c)		0.5 I $w^{2}$
d)		0.5 I $w^{2}$ + 0.5m $v^{2}$

30. The M.I of a uniform circular disc of mass M and radius R rotating about an axis passing through its centre and Ir to the plane of the disc is

a)		0.25M $R^{2}$
b)		M $R^{2}$
c)		2M $R^{2}$
d)		0.5M $R^{2}$

31. A hoop of mass M and radius R is suspended on a peg in a wall.Its moment of inertia about the peg is

a)		2M $R^{2}$
b)		M $R^{2}$
c)		$\frac{M R^{2}}{2}$
d)		3/2 M $R^{2}$

32. The reduced mass of the system of two particles of mass M and 2M will be

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

33. Two identical balls each of radius 10 cm are placed touching each other.The distance of their centre of mass from the point of contact is

a)		5 cm
b)		10 cm
c)		15 cm
d)		zero

34. If the resultant of all external forces is zero.The velocity of centre of mass will be

a)		Zero
b)		Constant
c)		either (a) or(b)
d)		neither (a) nor (b)

35. A grindstone has moment of inertia 6 ${kgm}^{2}$ about its axis. A constant torque is applied and the grindstone is found to aquire a speed of 150rpm 10 second after starting from rest. The torque is

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

36. Speed of the tip of the second hand of a watch of length 1cm is

a)		$(π / 15) {cms}^{- 1}$
b)		$(π / 30) {cms}^{- 1}$
c)		$(π / 60) {cms}^{- 1}$
d)		$(π / 90) {cms}^{- 1}$

37. A curve in a frictionless road has radius R. In order that a car moving with speed $υ$ should negotiate it without any tendency to slip sideways, the ' banking anlge' should be

a)		$\sin^{- 1} (v^{2} / Rg)$
b)		$\tan^{- 1} (v^{2} / Rg)$
c)		$\tan^{- 1} (Rg / v^{2})$
d)		$\cos^{- 1} (Rg / v^{2})$

38. The linear velocity of a point on the rim of a rotating wheel is three times greater than the linear velocity of a point 10cm closer to the wheel axis. The radius of the wheel is

a)		17.3 cm
b)		30 cm
c)		15 cm
d)		20 cm

39. A stone of mass 1 kg tied to a light inextensible string of length (10/3)m is whirled in a vertical circle. If the ratio of the maximum tension to minimum tension in the string is 4, and if g = 10 ${ms}^{- 2}$ ,the speed of the stone at the highest point is

a)		$10 \sqrt{3} {ms}^{- 1}$
b)		$10$ ${ms}^{- 1}$
c)		$20 \sqrt{2} {ms}^{- 1}$
d)		$5 {ms}^{- 1}$

40. An electric fan has blades of length 30 cm as measured from the axis of rotation. If the fan is rotating at 1,200 r.p.m, the acceleration of a point on the tip of the blade is about

a)		5,005 ${ms}^{- 2}$
b)		4, 740 ${ms}^{- 2}$
c)		2,370 ${ms}^{- 2}$
d)		1,600 ${ms}^{- 2}$

41. Moment of interia of a thin rod about one end and perpendicular to the length is given by

a)		$M l^{2} / 12$
b)		$M l / 2$
c)		$M l^{2} / 8$
d)		$M l^{2} / 3$

42. A sphere rolls on a plane surface. The ratio of its kinetic energy of rotation to its total KE is

a)		2 : 7
b)		2 : 5
c)		1 : 3
d)		1 : 6

43. A mass M is moving with a constant velocity parallel to the X-axis. Its angular momentum with respect to the origin

a)		is zero
b)		remains constant
c)		goes on increasing
d)		goes on decreasing

44. A fly wheel which is rotating at 1800 r.p.m comes to rest in 10 minutes. The angular acceleration is

a)		$π / 60 rad / s^{2}$
b)		$π / 10 rad / s^{2}$
c)		$π / 180 rad / s^{2}$
d)		$π rad / s^{2}$

45. A particle performs circular motion with angular momentum L. If the frequency of the particle is doubled and kinetic energy halved, the angular momentum is

a)		( $π / 60$ )2L
b)		( $π / 10$ )4L
c)		( $π / 180$ )L/2
d)		$π$ L/4

46. The moment of inertia of a body about a given axis is 1.2 $kg m^{2}$ . Initially the body is at rest. In order to produce a rotational KE 1500J, an angular acceleration of 25 $rad / s^{2}$ must be given for a period of

a)		8 s
b)		4 s
c)		5 s
d)		10 s

47. A particle of mass m = 5 units is moving in the X-Y plane along a line y = x+4 with velocity v = $3 \sqrt{2}$ . The magnitude of the angular momentum of the particle about the origin is

a)		75 units
b)		zero
c)		40 $\sqrt{2}$ units
d)		60 units

48. A sphere rolls on a horizontal plane with out slipping. The percentage of kinetic energy which is rotational is approximately

a)		28%
b)		8.3%
c)		72%
d)		100%

49. A metal sphere of radius 'r' and specific heat capacity 'c' is being rotated at a speed of 'n' r.p.s. It is suddenly stopped and 50% of the energy is converted in to heat. The rise in temperature is

a)		$\frac{2 π^{2} n^{2} r^{2}}{3 c}$
b)		$\frac{2 r^{2} n^{2} π^{2}}{5 c}$
c)		$\frac{4 π^{2} n^{2} r^{2}}{5 c}$
d)		$\frac{5 π^{2} n^{2} r^{2}}{4 c}$

50. A thin uniform rod of length $l$ and linear density $ρ$ rotates with angular velocity $ω$ about an axis perpendicular to the axis and passing through the mid point. The kinetic energy of rotation is

a)		$ρ l^{3} ω^{2} / 24$
b)		$ρ l^{3} ω^{2} l / 22$
c)		$2 y ρ ω^{2} l^{2} 24^{2} l^{2}$
d)		$ρ l^{2} ω^{2} l / 12$