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

Physics - Systems Particles Rotational Motion - Quiz-9

Two rotating bodies A and B of masses m and 2m with moments of inertia $I_{A}$ and $I_{B} (I_{B} > I_{A})$ have equal kinetic energy of rotation. If $L_{A}$ and $L_{B}$ be their angular momenta respectively, then:

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$L_{A} = \frac{L_{B}}{2}$
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$L_{A} = 2 L_{B}$
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$L_{B} > L_{A}$
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$L_{A} > L_{B}$

A solid sphere of mass m and radius R is rotating about its diameter. A soild cyclinder of the same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation $(E_{s p h e r e} / E_{c y l i n d e r})$ will be

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() 2:3
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() 1:5
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() 1:4
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() 3:1

A light rod of length l has two masses $m_{1} a n d m_{2}$ attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is

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$\frac{m_{1} m_{2}}{m_{1} + m_{2}} l^{2}$
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$\frac{m_{1} + m_{2}}{\sqrt{m_{1} m_{2} l^{2}}} l^{2}$
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$(m_{1} + m_{2}) l^{2}$
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$\sqrt{m_{1} m_{2} l^{2}}$

From a disc of radius R and mass M, a circular hole of diameter R, whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis, passing through the centre ?

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$13 M R^{2} / 32$
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$11 M R^{2} / 32$
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$9 M R^{2} / 32$
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$15 M R^{2} / 32$

A rod of weight w is supported by two parallel knife edges A and B and is in equilibrium in a horizontal position. The knives are at a distance d from each other. The centre of mass of the rod is at distance x from A. The normal reaction on A is

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$\frac{wx}{d}$
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$\frac{wd}{x}$
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w(d-x)/x
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$\frac{w (d - x)}{d}$

Two particles A and B. move with constant velocities v₁ and v₂. At the initial moment, their position vectors are $r_{1}$ and $r_{2}$ respectively. The condition for particles A and B for their collision is-

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$\frac{r_{1} - r_{2}}{|r_{1} - r_{2}|} = \frac{v_{2} - v_{1}}{|v_{2} - v_{1}|}$
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$r_{1} \cdot v_{1} = r_{2} \cdot v_{2}$
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_{$r_{1} \times v_{1} = r_{2} \times v_{2}$}
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r₁-r₂=v₁-v₂

A force F= $a \hat{i}$ $+ 3 \hat{j}$ $+ 6 \hat{k}$ is acting at a point r= $2 \hat{i}$ - $6 \hat{j}$ -12 $\hat{k}$ . The value of αfor which angular momentum is conserved about the origin is:

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-1
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2
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zero
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1

An automobile moves on a road with a speed of 54 km h^-1. The radius of its wheels is 0.45 m and the moment of inertia of the wheel about its axis of rotation is 3 kg m². If the vehicle is brought to rest in 15 s, the magnitude of average torque transmitted by its brakes to the wheel is

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6.66 kgm²s^-2
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8.58 kgm²s^-2
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10.86 kgm²s^-2
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2.86 kgm²s^-2

The force F acting on a particle of mass m is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from zero to 8 s is -

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24 Ns
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20 Ns
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12 Ns
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6 Ns

A body of mass (4m) is lying in xy-plane at rest. It suddenly explodes into three pieces. Two pieces each of mass (m) move perpendicular to each other with equal speeds (v). The total kinetic energy generated due to explosion is

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mv²
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3/2mv²
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2mv²
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4mv²

A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis.A massless string is wound round the cylinder with one end attached to it and other hanging freely.Tension in the string required to produce an angular acceleration of 2 rev/ s² is

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25N
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50N
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78.5N
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157N

The ratio of the accelerations for a solid sphere (mass m and radius R) rolling down an incline of angle θ without slipping and slipping down the incline without rolling is

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5:7
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2:3
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2:5
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7:5

An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of 12 ms^-1 and the second part of mass 2kg moves with 8 ms^-1 speed. If the third part flies off with 4 ms^-1 speed, then its mass is

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3kg
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5kg
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7kg
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17kg

When a mass is rotating in a plane about a fixed point, its angular momentum is directed along

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a line perpendicular to the plane of rotation
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the line making an angle of $45 °$ to the plane of rotation
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the radius
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the tangent to the orbit

Two persons of mass 55 kg and 65 kg respectively, are at the opposite ends of a boat.The length of the boat is 3.0m and weighs 100 kg.The 55 kg man walks up to the 65 kg man and sits with him.If the boat is in still water the centre of mass of the system shifts by

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3.0m
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2.3m
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zero
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0.75m

Two spheres A and B of masses $m_{1} a n d m_{2}$ respectively collide. A is at rest initially and B is moving with velocity v along x-axis. After collision B has a velocity $\frac{v}{2}$ in a direction perpendicular to the original direction.The mass A moves after collision in the direction

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same as that of B
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opposite to that of B
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$θ = \tan^{- 1} (\frac{1}{2}) t o t h e x ‐ a x i s$
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$θ = \tan^{- 1} (\frac{- 1}{2}) t o t h e x ‐ a x i s$

The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through:

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B
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C
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D
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A

Three masses are placed on the x-axis: 300 g at the origin, 500 g at x = 40 cm, and 400 g at x = 70 cm. The distance of the center of mass from the origin is:

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40 cm
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45 cm
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50 cm
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30 cm

The moment of inertia of a thin uniform rod of

mass M and length L about an axis passing

through its mid-point and perpendicular to its

length is $I_{0}$ . Its moment of inertia about an

axis passing through one of its ends and

perpendicular to its length is

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$I_{0} + {ML}^{2} / 4$
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$I_{0} + 2 {ML}^{2}$
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$I_{0} + {ML}^{2}$
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$I_{0} + {ML}^{2} / 2$

A mass m moving horizontally (along the x-axis) with velocity v collides and sticks to mass of 3m moving vertically upward (along the y-axis) with velocity 2v. The final velocity of the combination is

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$\frac{1}{4} v \hat{i} + \frac{3}{2} v \hat{j}$
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$\frac{1}{3} v \hat{i} + \frac{2}{3} v \hat{j}$
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$\frac{2}{3} v \hat{i} + \frac{1}{3} v \hat{j}$
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$\frac{3}{2} v \hat{i} + \frac{1}{4} v \hat{j}$

A circular disk of moment of inertia $I_{t}$ is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed $ω_{i} .$ Another disk of moment of inertia $I_{b}$ is dropped coaxially onto the rotation disk. Initially the second disk has zero angular speed. Eventually both the disks rotate with a constant angular speed $ω_{f} .$ The energy lost by the initially rotating disc to friction is

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$\frac{1}{2} \frac{I_{b}^{2}}{(I_{t} + I_{b})} ω_{i}^{2}$
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$\frac{1}{2} \frac{I_{t}^{2}}{(I_{t} + I_{b})} ω_{i}^{2}$
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$\frac{1}{2} \frac{I_{b} - I_{t}}{(I_{t} + I_{b})} ω_{i}^{2}$
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$\frac{1}{2} \frac{I_{b} I_{t}}{(I_{t} + I_{b})} ω_{i}^{2}$

A ball moving with velocity $2 m s^{- 1}$ collides head on with another stationery ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in $m s^{- 1}$ ) after collision will be

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0,1
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1,1
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1,0.5
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0,2

A man of 50 kg mass is standing in a gravity free space at a height of 10m above the floor. He throws a stone of 0.5 kg mass downwards with a speed $2 m s^{- 1} .$ When the stone reaches the floor, the distance of the man above the floor will be

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9.9m
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10.1m
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10m
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20m

From a circular disc of radius R and mass 9M, a small disc of mass M and radius $\frac{R}{3}$ is removed concentrically. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through its centre is:

(a) $\frac{40}{9} M R^{2}$ (b) $M R^{2}$

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1
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2
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3
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4

An explosion blows a rock into three parts. Two parts go off at right angles to each other. These two are, 1 kg first part moving with a velocity of $12 {ms}^{- 1}$ and 2 kg second part moving with a velocity of $8 {ms}^{- 1} .$ If the third part flies off with a velocity of $4 {ms}^{- 1},$ its mass would be

(a) $5 kg$ (b) $7 kg$

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1
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2
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3
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4

If $\vec{F}$ 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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() $\vec{r} . \vec{τ} \neq 0 and \vec{F} . \vec{τ} = 0$
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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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() $\vec{r} . \vec{τ} = 0 and \vec{F} . \vec{τ} \neq 0$

Two bodies of mass 1kg and 3kg have position vectors $\hat{i} + 2 \hat{j} + \hat{k}$ and $- 3 \hat{i} - 2 \hat{j} + \hat{k}$ , respectively. The centre of mass of this system has a position vector -

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

Four identical thin rods each of mass M and length t, form a square frame. Moment of inertia of this frame about an axis through the centre of the square and perpendicular to its plane is

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$\frac{4}{3} M t^{2}$
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$\frac{2}{3} M t^{2}$
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$\frac{13}{3} M t^{2}$
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$\frac{1}{3} M t^{2}$

A shell of mass 200g is ejected from a gun of mass 4 kg by an explosion that generates 1.05 kJ of energy. The initial velocity of the shell is -

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40 $m s^{- 1}$
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120 $m s^{- 1}$
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100 $m s^{- 1}$
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80 $m s^{- 1}$

A thin rod of length L and mass M is bent at its midpoint into two halves so that the angle between them is $90^{°}$ . The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is

(a) $\frac{M L^{2}}{24}$

(b) $\frac{M L^{2}}{12}$

(d) $\frac{\sqrt{2} M L^{2}}{24}$

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1
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2
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3
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4

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Practice Physics Quiz Questions and Answers

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Practice Physics Quiz Questions and Answers

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