A solid cylinder of mass 3 kg is rolling on a horizontal surface with a velocity of 4 ms -1 . It collides with a horizontal spring of force constant 200 Nm -1 . The maximum compression produced in the spring will be:

If F → is the force acting on a particle having position vector r → and τ → be the torque of this force about the origin, then:

r → . τ → = 0 and F → . τ → = 0

r → . τ → ≠ 0 and F → . τ → = 0

r → . τ → > 0 and F → . τ → < 0

r → . τ → = 0 and F → . τ → ≠ 0

A sphere collides elastically and obliquely to another stationary identical sphere. If v → 1 and v → 2 are their velocities after collision then v → 1 . v → 2 is

Depends on the impact parameter

Physics - Systems Particles Rotational Motion - Quiz-10

A moving block having mass m collides with another stationary block having a mass of 4m. The lighter block comes to rest after the collision. When the initial velocity of the lighter block is v, then the value of the coefficient of restitution (e) will be:

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0.5
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0.25
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0.8
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0.4

Three objects, A : (a solid sphere), B : (a thin circular disk) and C = (a circular ring), each have the same mass M and radius R. They all spin with the same angular speed about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation:

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W_C > W_B > W_A
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W_A > W_B > W_C
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W_B > W_A > W_C
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W_A > W_C > W_B

Which of the following statements are correct?
(a) Centre of mass of a body always coincides with the centre of gravity of the body
(b) Centre of gravity of a body is the point about which the total gravitational torque on the body is zero
(c) A couple on a body produce both translational and rotation motion in a body
(d) Mechanical advantage greater than one means that small effort can be used to lift a large load

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(a) and (b)
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(b) and (c)
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(c) and (d)
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(b) and (d)

The moment of the force, $\vec{F} = 4 \hat{i} + 5 \hat{j} - 6 \hat{k}$ at point (2, 0, -3) about the point (2, -2, -2) is given by:

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$- 8 \hat{i} - 4 \hat{j} - 7 \hat{k}$
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$- 4 \hat{i} - \hat{j} - 8 \hat{k}$
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$- 7 \hat{i} - 8 \hat{j} - 4 \hat{k}$
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$- 7 \hat{i} - 4 \hat{j} - 8 \hat{k}$

A solid sphere is in rolling motion. In rolling motion, a body possesses translational kinetic energy (K_t) as well as rotational kinetic energy (K_r) simultaneously. The ratio K_t: (K_t + K_r) for the sphere will be:

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7:10
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5:7
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10:7
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2:5

A uniform circular disc of radius 50 cm at rest is free to turn about an axis that is perpendicular to its plane and passes through its centre. It is subjected to a torque that produces a constant angular acceleration of 2.0 rad s^-2. Its net acceleration in ms^-2 at the end of 2.0 s is approximately:

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7
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6
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3
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8

A mass m moves in a circle on a smooth horizontal plane with velocity v₀ at a radius R₀. The mass is attached to a string that passes through a smooth hole in the plane as shown.

The tension in the string is increased gradually and finally m moves in a circle of radius

\frac{R_{0}}{2}

. The final value of the kinetic energy is:

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$m v_{0}^{2}$
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$\frac{1}{4} m v_{0}^{2}$
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2 $m v_{0}^{2}$
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$\frac{1}{2} m v_{0}^{2}$

Three identical spherical shells, each of mass m and radius r are placed as shown in the figure. Consider an axis XX', which is touching two shells and passing through the diameter of the third shell. The moment of inertia of the system consisting of these three spherical shells about the XX' axis is:

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$\frac{11}{5} m r^{2}$
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$3 m r^{2}$
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$\frac{16}{5} m r^{2}$
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$4 m r^{2}$

2. 0.6 m

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0.5 m
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4. 0.2 m
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0.7 m
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A solid cylinder of mass 3 kg is rolling on a horizontal surface with a velocity of 4 ms^-1. It collides with a horizontal spring of force constant 200 Nm^-1. The maximum compression produced in the spring will be:

Two particles that are initially at rest, move towards each other under the action of their mutual attraction. If their speeds are v and 2v at any instant, then the speed of the centre of mass of the system will be:

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2v
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0
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1.5v
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v

\vec{F}

is the force acting on a particle having position vector

\vec{r}

and

\vec{τ}

be the torque of this force about the origin, then:

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$\vec{r}$ . $\vec{τ}$ ≠ 0 and $\vec{F}$ . $\vec{τ}$ = 0
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$\vec{r}$ . $\vec{τ}$ > 0 and $\vec{F}$ . $\vec{τ}$ < 0
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$\vec{r}$ . $\vec{τ}$ = 0 and $\vec{F}$ . $\vec{τ}$ = 0
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$\vec{r}$ . $\vec{τ}$ = 0 and $\vec{F}$ . $\vec{τ}$ ≠ 0

The ratio of the radii of gyration of a circular disc to that of a circular ring, each of the same mass and radius, around their respective axes is:

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$\sqrt{3} : \sqrt{2}$
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$1 : \sqrt{2}$
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$\sqrt{2} : 1$
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$\sqrt{2} : \sqrt{3}$

The moment of inertia of a uniform circular disc of radius R and mass M about an axis touching the disc at its diameter and normal to the disc is:

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$M R^{2}$
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$\frac{2}{5} M R^{2}$
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$\frac{3}{2} M R^{2}$
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$\frac{1}{2} M R^{2}$

A solid cylinder of mass 2 kg and radius 4 cm is rotating about its axis at the rate of 3 rpm. The torque required to stop after 2 $π$ revolutions is:

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$2 \times 10^{6} N m$
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$2 \times 10^{- 6} N m$
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$2 \times 10^{- 3} N m$
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$12 \times 10^{- 4} N m$

The angular displacement( $θ$ ) of the blades of
a ceiling fan, when the fan is switched on at
t = 0, is shown in figure. The average angular
velocity of the fan blades during the first 8
seconds will be

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40 $π$ rad/s
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20 $π$ rad/s
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10 $π$ rad/s
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5 $π$ rad/s

A body of mass $m_{1}$ moving with uniform velocity of 40 m/s collides with another mass $m_{2}$ at rest and then the two together begin to move with uniform velocity of 30 m/s. The ratio of their masses $\frac{m_{1}}{m_{2}}$ is

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0.75
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1.33
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3.0
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4.0

A ball of mass m moving with a speed u undergoes a head-on elastic collision with a ball of mass nm initially at rest. The fraction of initial energy transferred to the heavier ball is

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$\frac{n}{1 + n}$
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$\frac{n}{{(1 + n)}^{2}}$
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$\frac{2 n}{{(1 + n)}^{2}}$
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$\frac{4 n}{{(1 + n)}^{2}}$

A sphere of mass m moving horizontally with velocity $v_{0}$ collides against a pendulum bob of mass m. If the two masses stick together after the collision, then the maximum height attained is

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$\frac{v_{0}^{2}}{2 g}$
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$\frac{v_{0}^{2}}{4 g}$
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$\frac{v_{0}^{2}}{6 g}$
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$\frac{v_{0}^{2}}{8 g}$

An object flying in the air with velocity $(20 \hat{i} + 25 \hat{j} - 12 \hat{k})$ suddenly breaks into two pieces whose masses are in the ratio of 1:5. The smaller mass flies off with a velocity $(100 \hat{i} + 35 \hat{j} + 8 \hat{k})$ . The velocity of the larger piece will be:

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$4 \hat{i} + 23 \hat{j} - 16 \hat{k}$
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$- 100 \hat{i} - 35 \hat{j} - 8 \hat{k}$
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$20 \hat{i} + 15 \hat{j} - 80 \hat{k}$
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$- 20 \hat{i} - 15 \hat{j} - 80 \hat{k}$

A particle of mass 5m at rest suddenly breaks on its own into three fragments. Two fragments of mass m each move along with mutually perpendicular directions with speed v each. The energy released during the process is,

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$\frac{3}{5} m v^{2}$
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$\frac{5}{3} m v^{2}$
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$\frac{3}{3} m v^{2}$
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$\frac{4}{3} m v^{2}$

A solid cylinder of mass 2 kg and radius 50 cm rolls up an inclined plane of the angle of inclination $30^{°}$ . The centre of mass of the cylinder has a speed of 4 m/s. The distance travelled by the cylinder on the inclined surface will be, $[t a k e g = 10 m / s^{2}]$

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2.2 m
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1.6 m
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1.2 m
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2.4 m

A ball strikes the floor at an angle of $45^{o}$ with vertical and rebounds of an angle of 60° with the vertical. Assuming the contact to be smooth the coefficient of restitution is

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1
0%

$\frac{1}{\sqrt{2}}$
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$\frac{1}{3}$
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$\frac{1}{\sqrt{3}}$

A ball of mass 2 kg is at rest on a horizontal smooth surface. Another ball of the same mass hit the first ball at an angle of 60° with the horizontal. At the time of the collision, the velocity of the second ball is 20 m/s. If the collision is perfectly inelastic and after the collision, both the balls stick together, then the speed of the combined balls is:

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Zero
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2.5 m/s
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10 m/s
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5 m/s

A bullet is fired from a gun. Assuming that the gun recoils freely, the kinetic energy of the bullet is

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less than the kinetic energy of the gun.
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equal to the kinetic energy of the gun.
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more than the kinetic energy of the gun.
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equal to or less than the kinetic energy of the gun.

Two blocks having equal masses stick together after the collision. If their combined velocity after the collision is equal to the arithmetic mean velocity of them before the collision, then the coefficient of restitution is:

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Zero
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0.5
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0.8
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1

A sphere collides elastically and obliquely to another stationary identical sphere. If ${\vec{v}}_{1} and {\vec{v}}_{2}$ are their velocities after collision then ${\vec{v}}_{1} . {\vec{v}}_{2}$ is

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Zero
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Positive
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Negative
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Depends on the impact parameter

Choose incorrect statement about the oblique collision of two bodies.

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The momentum of each body is conserved along the tangent.
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The momentum of the system is conserved.
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The momentum of each body is conserved along common normal.
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Coefficient of restitution is considered along the common normal.

An ideal horizontal spring has been compressed by two masses of 1 kg and 4 kg at its ends placed on a frictionless table. The stored energy is 40 joule. If the spring is released, the lighter mass will acquire a speed of:

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2 m/s
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4 m/s
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8 m/s
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16 m/s

A body of mass m strikes with the ground with speed u and coefficient of restitution is e, then find the work done by normal reaction force on the body.

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zero
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$\frac{1}{2} {mu}^{2} (e^{2} - 1)$
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$\frac{1}{2} {mu}^{2} (1 - e^{2})$
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$\frac{1}{2} {mu}^{2}$

A ball is dropped from a height h on a stationary floor and rebounds. If the coefficient of restitution is 0.5, then the total distance covered by the ball before it strikes the floor for 3rd time is:

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2h
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$\frac{13 h}{8}$
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$\frac{3 h}{2}$
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$\frac{4 h}{3}$

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Practice Physics Quiz Questions and Answers

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Practice Physics Quiz Questions and Answers

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