Physics - Systems Particles Rotational Motion - Quiz-5

$M o m e n t o f i n e r t i a o f a d i s c a b o u t i t s o w n a x i s i s I . I t s M O I a b o u t a \tan g e n t i a l a x i s i n i t s p l a n e i s : (A) \frac{5}{2} I (B) 3 I (C) \frac{3}{2} I (D) 4 I$

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1
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2
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3
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4

A rigid body rotates with an angular momentum L. If its rotational kinetic energy is made 4 times, its angular momentum will become

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4L
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16L
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$\sqrt{2} L$
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2L

Four particles of mass $m_{1} = 2 m, m_{2} = 4 m, m_{3} = m, and m_{4}$ are placed at the four corners of a square. What should be the value of $m_{4}$ so that the center of mass of all the four particles is exactly at the center of the square?

Four particles of mass m1 = 2m, m2 = 4m, m3 = m and m4 are placed at four corners of a square. What should be the value of m4 so that

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2m
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2, 8m
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6m
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None of these

Angular momentum of a body is defined as the product of

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Mass and angular velocity
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Centripetal force and radius
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Linear velocity and angular velocity
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Moment of inertia and angular velocity

Two masses $m_{1} and m_{2}, m_{1} > m_{2}$ are connected to the ends of massless rope and allowed to move as shown in the figure. The acceleration of the centre of mass assuming pulley is massless and frictionless, is

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$\frac{m_{1} - m_{2}}{m_{1} + m_{2}} g$
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0
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${(\frac{m_{1} - m_{2}}{m_{1} + m_{2}})}^{2} g$
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${(\frac{m_{1} + m_{2}}{m_{1} - m_{2}})}^{2} g$

The speed of a uniform spherical shell after rolling down an inclined plane of vertical height h from rest is:

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$\sqrt{\frac{10 g h}{7}}$
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$\sqrt{\frac{6 g h}{5}}$
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$\sqrt{\frac{4 g h}{5}}$
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$\sqrt{2 g h}$

Two identical balls marked 2 and 3. in contact with each other and at rest on a horizontal frictionless table, are hit head-on by another identical ball marked 1 moving initially with a speed v as shown in the figure. Assume the collision is elastic, then mark out the correct statement.

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2. Bll 1 and 2 come to rest and ball 3 moves with speed v
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1.&nsp; Ball 1 comes to rest and ball 2 and 3 moves with speed v
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3 Eah ball moves with speed
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4. None of the above

A uniform rod of mass m is bent into the form of a semicircle of radius R. The moment of inertia of the rod about an axis passing thorugh A and Perpendicular to the plane of paper is

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$\frac{2}{3} M R^{2}$
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$M R^{2}$
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2 $M R^{2}$
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$\frac{3}{2} M R^{2}$

A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity $ω$ . Four objects each of mass m, are kept gently to the opposite ends of two perpendicular diameters of the ring. The angular velocity of the ring will be

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$\frac{M ω}{M + 4 m}$
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$\frac{(M + 4 m) ω}{M}$
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$\frac{(M - 4 m) ω}{M + 4 m}$
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$\frac{M ω}{4 m}$

Let g be acceleration due to gravity on the surface of earth and T be the rotational kinetic energy of the earth. Suppose the earth's radius decreases by 2%. Keeping all other quantities same (even $ω$ )

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g decreases by 2% and T decreases by 4%
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g decreases by 4% and T decreases by 2%
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g increases by 4% and T decreases by 4%
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g decreases by 4% and T increases by 4%

The angular momentum of a system of particles is conserved

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when no external force acts upon the system
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when no external torque acts upon the system
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when no external impulse acts upon the system
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when axis of rotation remains same

One hollow and one solid cylinder of the same radius roll down on a smooth inclined plane. Then the foot of the inclined plane is reached by

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solid cylinder earlier
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hollow cylinder earlier
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simultaneously both
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the heavier earlier irrespective of being solid or hollow

A closed tube partly filled with water lies in a horizontal plane. If the tube is rotated about perpendicular bisector, the moment of inertia of the system

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increases
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decreases
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remains constant
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depends on sense of rotation

A disc is rotating With an angular speed of m. If a child sits on it, which of the following is conserved?

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kinetic energy
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potential energy
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linear momentum
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angular momentum

ABC is an equilateral triangle with O as its cente. ${\vec{F}}_{1}, \vec{F_{2}} a n d \vec{F_{3}}$ represent three forces acting along the sides AB, BC and AC respectively. If the total torque about O is zero then the magnitude of $\vec{F_{3}}$ is

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$F_{1} + F_{2}$
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$F_{1} - F_{2}$
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$\frac{F_{1} + F_{2}}{2}$
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$2 (F_{1} + F_{2})$

A circular platform is mounted a frictionless vertical axle. Its radius R = 2m and moment of inertia about the axle are 200 ${kgm}^{2}$ . It is initially at rest. A 50 kg man on the edge of the platform and begins to walk along the edge at the speed of 1 $m s^{- 1}$ relative to the ground. Time taken by the man to complete one revolution is

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$πs$
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$\frac{3 π}{2} s$
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$2 πs$
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$\frac{π}{2} s$

The motor of an engine is rotating about its axis with an angular velocity of 100 rpm. It comes to rest is 15 s, after being switched off. Assuming constant angular deceleration. What are the numbers of revolutions made by it before coming to rest?

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12.5
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40
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32.6
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15.6

A T joint is formed by two identical rods A and B each of mass m and length L in the XY plane as shown. Its moment of inertia about axis passing through A and perpendicular to the plane of the joint,

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$\frac{2 {mL}^{2}}{3}$
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$\frac{{mL}^{2}}{12}$
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$\frac{{mL}^{2}}{6}$
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None of these

A hollow sphere of diameter 0.2 m and mass 2 kg is rolling on an inclined plane with velocity v = 0.5 m/ s. The kinetic energy of the sphere is

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0.1 J
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0.3 J
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0.5 J
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0.42 J

A man of the mass M stands at one end of a plank of length L which lies at rest on a frictionless surfacé. The man walks to the other end of the plank. If the mass of the plank is $\frac{M}{3}$ , the distance that the man moves relative to the ground is

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$\frac{3 L}{4}$
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$\frac{L}{4}$
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$\frac{4 L}{5}$
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$\frac{L}{3}$

Ratio of total kinetic energy and rotational kinetic energy in the motion of a disc is

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1:1
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2:7
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1:2
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3:1

A bomb of mass 9 kg explodes into two pieces of mass 3 kg and 6 kg. The velocity of 3 kg mass is 16 m/s. The velocity of 6 kg mass is

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4 m/s
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8 m/s
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16 m/s
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32 m/s

A cylinder is rolling over a surface. Which points on it move rectilinearly?

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All points on the curved surface of the cylinder.
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All points on the flat surfaces of the cylinder.
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All points on the axis of the cylinder.
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None of the above

A uniform rod AB of length l and mass m is free to rotate about point A. The rod is released from rest in horizontal position. Given that the moment of inerita of the rod about A is $\frac{{ml}^{2}}{3}$ the initial angular acceleration of the rod will be

$1 . \frac{2 g}{3 l} 2 . mg \frac{l}{2} 3 . \frac{3}{2} gl 4 . \frac{3 g}{2 l}$

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1
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2
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3
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4

The magnitude of the impulse developed by a mass of 0.2 kg which changes its velocity from $5 \hat{i} - 3 \hat{j} + 7 \hat{k} m / s to 2 \hat{i} + 3 \hat{j} + \hat{k} m / s$ is

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2.7 N-s
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1.8 N-s
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0.9 N-s
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3.6 N-s

A round disc of the moment of inertia $l_{2}$ about its axis perpendicular to its plane and passing through its center is placed over another disc of the moment of inertial $l_{1}$ rotating with an angular velocity $ω$ about the same axis. The final angular velocity of the combination of discs is

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$\frac{l_{2} ω}{l_{1} + l_{2}}$
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$ω$
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$\frac{l_{1} ω}{l_{1} + l_{2}}$
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$\frac{(l_{1} + l_{2}) ω}{l_{1}}$

A light cord is wrapped around the rim of the wheel disc of radius r and a steady downward pull F is exerted on the cord, then the angular acceleration of the wheel is

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$\frac{F}{M r}$
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$\frac{2 F}{M}$
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$\frac{2 F}{M r}$
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$\frac{M}{2 F}$

Which of the following will not be affected if the radius of the sphere is increased while keeping mass constant?

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Moment of inertia
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Angular momentum
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Angular velocity
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Rotational kinetic energy

A particle of mass 5 g is moving with a uniform speed of $3 \sqrt{2}$ cm/s in the x-y plane along the line y = $2 \sqrt{5}$ cm. The magnitude of its angular momentum about the origin in $g - {cm}^{2} / s$ is

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0
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30
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$30 \sqrt{2}$
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$30 \sqrt{10}$

A mass M is supported by a massless string wound round a uniform cylinder of mass M and radius R. On releasing the mass from rest, it will fall with an acceleration assuming no slipping-

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$\frac{g}{3}$
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$\frac{g}{2}$
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$\frac{2 g}{3}$
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g

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Practice Physics Quiz Questions and Answers

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Practice Physics Quiz Questions and Answers

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