The position of a particle is given by r ⇀ = 1 ^ + 2 j ^ - k ^ and momentum P → = 3 i ^ + 4 j ^ - 2 k ^ . The angular momentum is perpendicular to:

Line at equal angles to all the three axes

Physics - Systems Particles Rotational Motion - Quiz-4

If a force acts on a body at a point away from the centre of mass, then

0%

Linear acceleration changes
0%

Angular acceleration changes
0%

Both change
0%

None of these

A sphere can not roll on:

0%

a smooth horizontal surface
0%

a rough horizontal surface
0%

a smooth inclined surface
0%

a rough inclined surface

Two balls are thrown simultaneously in the air. The acceleration of the center of mass of the two balls while in air

0%

depends on the direction of the motion of the balls
0%

depends on the masses of the two balls
0%

depends on the speeds of two balls
0%

is equal to g

A cord is wound round the circumference of wheel of radius r. The axis of the wheel is horizotal and moment of inertia about it is I. A weight mg is attached to the end of the cord and falls from rest. After falling through a distance h, the angular velocity of the wheel will be

0%

$\sqrt{\frac{2 g h}{I + m r}}$
0%

$\sqrt{\frac{2 m g h}{I + m r^{2}}}$
0%

${[\frac{2 m g h}{I + 2 m}]}^{\frac{1}{2}}$
0%

$\sqrt{2 g h}$

If a body of mass m collides head on, elastically with velocity u with another identical body at rest. After collision velocity of the second body will be

0%

zero
0%

u
0%

2u
0%

data insufficient

A particle of mass m at rest is acted upon by a constant force F for a time t. Its kinetic energy after an interval t is

0%

$\frac{F^{2} t^{2}}{m}$
0%

$\frac{F^{2} t^{2}}{2 m}$
0%

$\frac{F^{2} t^{2}}{3 m}$
0%

$\frac{Ft}{2 m}$

If a person standing on a rotating disc stretches out his hands, the angular speed will

0%

increase
0%

decrease
0%

remain same
0%

None of these

If the earth were to suddenly contract to $\frac{1}{n}$ th of its present size without any change in its mass, the duration of the new day will be nearly

0%

24/n hours
0%

24 n hours
0%

24/ $n^{2}$ hours
0%

24 $n^{2}$ hours

A sqaure lamina is as shown in figure. The moment of inertia of the frame about the three axes shown in figure are $I_{1}, I_{2} a n d I_{3}$ respectively. Select the correct alternative.

0%

$I_{2} = I_{3} > I_{1}$
0%

$I_{1} > I_{2} > I_{3}$
0%

$I_{2} = I_{3} < I_{1}$
0%

$I_{1} < I_{2} < I_{3}$

Three interacting particles of masses 1.0 kg, 2.0 kg and 4.0 kg have each a velocity of 1 $m s^{- 1}$ magnitude along the positive direction of x, y and z-axis respectively. Due to forces of interaction third particle stops and the velocity of second particle becomes $2 \hat{j} + \hat{k} m s^{- 1}$ , the velocity of the first particle is

0%

$4 \hat{i} + \hat{j} + \hat{k}$
0%

$\hat{i} - 2 \hat{j} + 2 \hat{k}$
0%

$2 \hat{i} + 3 \hat{j} - \hat{k}$
0%

$- \hat{i} + 3 \hat{j} + \hat{k}$

A particle performs uniform circular motion with an angular momentum L. If the frequency of the particle motion is double, the angular momentum becomes

0%

2L
0%

4L
0%

$\frac{L}{2}$
0%

$\frac{L}{4}$

In figure (a), a meter stick, half of which is wood and the other half steel is pivoted at the wooden end at O and a force F is applied to the steel end a. In figure (b) the stick is pivoted at the steel eid at O' and the same force F is applied at the wooden end at a' The angular acceleration

0%

in (a) is greater than in (b)
0%

in (b) is greater than in (a)
0%

equal both in (a) and (b)
0%

none of the above.

A 20 kg solid disc rolls on a horizontal surface at the rate of 4 $m s^{- 1}$ . Its total kinetic energy is

0%

60 J
0%

120 J
0%

240 J
0%

80 J

From a uniform square plate of side a and mass m, a square portion DEFG of side $\frac{a}{2}$ is removed. Then, the moment of inertia of the remaining portion about the axis AB is:

0%

$\frac{7 {ma}^{2}}{16}$
0%

$\frac{3 {ma}^{2}}{16}$
0%

$\frac{3 {ma}^{2}}{4}$
0%

$\frac{9 {ma}^{2}}{16}$

Two bodies having masses $m_{1}$ and $m_{2}$ and velocities $u_{1}$ and $u_{2}$ collide form a composite system. If $m_{1}$ $u_{1}$ + $m_{2}$ $u_{2}$ = 0 ( $m_{1}$ $\neq$ $m_{2}$ ), the velocity of composite system will be

0%

$u_{1}$ - $u_{2}$
0%

$u_{1}$ + $u_{2}$
0%

$\frac{u_{1} + u_{2}}{2}$
0%

Zero

The centre of the mass of 3 particles, 10 kg, 20 kg, and 30 kg, is at (0, 0, 0). Where should a particle with a mass of 40 kg be placed so that its combined centre of mass is (3, 3, 3)?

0%

(0, 0, 0)
0%

(7.5, 7.5, 7.5)
0%

(1, 2, 3)
0%

(4, 4, 4)

The position of a particle is given by $\overset{⇀}{r} = (\hat{1} + 2 \hat{j} - \hat{k})$ and momentum $\vec{P} = (3 \hat{i} + 4 \hat{j} - 2 \hat{k})$ . The angular momentum is perpendicular to:

0%

X-axis
0%

Y-axis
0%

Z-axis
0%

Line at equal angles to all the three axes

A body falling vertically downward under gravity breaks into two parts of unequal masses. The center of mass of the parts taken together shifts horizontally towards

0%

heavier piece
0%

lighter piece
0%

does not shift horizontally
0%

depends on the vertical velocity at the time of breaking

A particle of mass m moves along line PC with velocity v as shown. What is the angular momentum of the particle about O

0%

mvL
0%

mvl
0%

mvr
0%

0

A solid sphere, disc, and solid cylinder all of the same mass and made up of the same material are allowed to roll down (from rest) on an inclined plane, then,

0%

Solid sphere reaches the bottom first
0%

Solid sphere reaches the bottom late
0%

The disc will reach the bottom first
0%

All of them reach the bottom at the same time

A cylinder of 500 g and radius 10 cm has moment of inertia (about its natural axis)

0%

$2.5 \times 10^{- 3} k g - m^{2}$
0%

$2 \times 10^{- 3} k g - m^{2}$
0%

$5 \times 10^{- 3} k g - m^{2}$
0%

$3.5 \times 10^{- 3} k g - m^{2}$

When a body is rolling without slipping on a rough horizontal surface, the work done by friction is

0%

Always zero
0%

May be zero
0%

Always positive
0%

Always negative

Two rings of the same radius and mass are placed such that their centers are at a common point and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the center and perpendicular to the plane of one of the rings is (mass of the ring and radius = r)

0%

$\frac{1}{2} {mr}^{2}$
0%

${mr}^{2}$
0%

$\frac{3}{2} {mr}^{2}$
0%

$2 {mr}^{2}$

In a rectangle ABCD (BC = 2AB). The moment of inertia along which axis will be minimum?

0%

BC
0%

BD
0%

HF
0%

EG

A wheel comprises of a ring of radius R and mass M and three spokes of mass m each. The moment of inertia of the wheel about its axis is

0%

$(M + \frac{m}{4}) R^{2}$
0%

$(M + m) R^{2}$
0%

$(M + 3 m) R^{2}$
0%

$(\frac{M + m}{2}) R^{2}$

The angular velocity of a body changes from $\frac{1}{25}$ rev./sec to 1 rev./sec. without applying any torque. The ratio of its radius of gyration in two situations is :

0%

5: 1
0%

1: 5
0%

1: 25
0%

25: 1

A solid cylinder and a solid sphere, both having the same mass and radius, are released from a rough inclined plane. Both roll without slipping. Then,

0%

the force of friction that acts on the two is the same
0%

the force of friction is greater in the case of a sphere than in a cylinder
0%

the force of friction is greater in the case of a cylinder than in a sphere
0%

the force of friction will depend on the nature of the surface of the body that is moving and that of the inclined surface and is independent of the shape and size of the moving body

A homogeneous disc of mass 2 kg and radius 15 cm is rotating about its axis (which is fixed) with an angular velocity of 4 rad/sec. The linear momentum Of the disc is

0%

1.2 kg m/sec
0%

1.0 kg m/sec
0%

0.6 kg m/sec
0%

None of these

A rigid body rotates about a fixed axis with a variable angular velocity equal to $α - β t$ , at the time t, where $α, β$ are constants. The angle through which it rotates before it stops is:

0%

$\frac{α^{2}}{2 β}$
0%

$\frac{α^{2} - β^{2}}{2 α}$
0%

$\frac{α^{2} - β^{2}}{2 β}$
0%

$\frac{(α - β) α}{2}$

For the uniform T shaped structure, with mass 3M, the moment of inertia about an axis normal to the plane and passing through O would be

0%

$\frac{2}{3} {MI}^{2}$
0%

${MI}^{2}$
0%

$\frac{{MI}^{2}}{3}$
0%

None of these

0:0:1

Practice Physics Quiz Questions and Answers

0:0:1

Practice Physics Quiz Questions and Answers

Support mcqexams.com by disabling your adblocker.