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What is called a rigid body?

Important Questions on Motion of System of Particles and Rigid Bodies

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Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Centre of Mass

Two spherical bodies of mass M and 5M and radii R and 2R released in free space with initial separation between their centres equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller body before collision is:

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Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Centre of Mass

Distance of the centre of mass of a solid uniform cone from its vertex is

z_{0}

. If the radius of its base is

R

and its height is

h

then

z_{0}

is equal to:

MEDIUM

Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Centre of Mass

A uniform thin rod AB of length

L

has linear mass density

μ (x) = a + \frac{b x}{L}

, where

x

is measured from A. If the CM of the rod lies at a distance of

(\frac{7}{12} L)

from A, then

a

and

b

are related as:

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Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Centre of Mass

A rod of length

L

has non-uniform linear mass density given by

ρ (x) = a + b {(\frac{x}{L})}^{2},

where

a

and

b

are constants and

0 \leq x \leq L

. The value of

x

for the centre of mass of the rod is at:

HARD

Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Centre of Mass

A solid cylinder P rolls without slipping from rest down an inclined plane attaining a speed

v_{P}

at the bottom. Another smooth solid cylinder

Q

of same mass and dimensions slides without friction from rest down the inclined plane attaining a speed

v_{Q}

at the bottom. The ratio of the speeds

(\frac{v_{Q}}{v_{P}})

is -

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Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Centre of Mass

A uniform rectangular thin sheet $A B C D$ of mass $M$ has length $a$ and breadth $b$ , as shown in the figure. If the shaded portion $H B G O$ is cut-off, the coordinates of the centre of mass of the remaining portion will be:

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Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Centre of Mass

The position vector of the center of mass

{\vec{r}}_{cm}

of an asymmetric uniform bar of negligible area of cross-section as shown in figure is:

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Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Centre of Mass

A circular hole of radius $(\frac{a}{2})$ is cut out of a circular disc of radius $a$ as shown in figure. The centroid of the remaining circular portion with respect to point $O$ will be:

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Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Centre of Mass

A solid sphere rolls without slipping, first horizontally and then up to a point $x$ at height $h$ on an inclined plane before rolling down, as shown in the figure below.

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The initial horizontal speed of the sphere is

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Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Centre of Mass

Consider two uniform discs of the same thickness and different radii

R_{1} = R

and

R_{2} = α R

made of the same material. If the ratio of their moments of inertia

I_{1}

and

I_{2}

, respectively, about their axes is

I_{1} : I_{2} = 1 : 16

then the value of

α

is :

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Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Centre of Mass

A square shaped hole of side $l = \frac{a}{2}$ is carved out at a distance $d = \frac{a}{2}$ from the centre $O$ of a uniform circular disk of radius $a$ . If the distance of the centre of mass of the remaining portion from $O$ is $- \frac{a}{x}$ , value of $x$ (to the nearest integer) is :

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Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Centre of Mass

V -

shaped rigid body has two identical uniform arms. What must be the angle between the two arms, so that when the body is hung from one end the other arm is horizontal?

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Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Centre of Mass

A uniform wire of length

L

' with centre of mass at the origin is lying along the

x

- axis. The wire is bent in the form of a circle such that its lowest point is at the origin. Then the shift of centre of mass is

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Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Centre of Mass

In a physical balance working on the principle of moments, when

5 mg

weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct?

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Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Centre of Mass

Figure shows a rectangular copper plate with its centre of mass at the origin $O$ and side $A B = 2 B C = 2 m .$ If a quarter part of the plate (shown as shaded) is removed, the centre of mass of the remaining plate would lie at

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Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Centre of Mass

Which of the following statements are correct?

(i) Centre of mass of a body always coincides with the centre of gravity of the body.

(ii) Centre of mass of a body is the point at which the total gravitational torque on the body is zero

(iii) A couple on a body produce both translational and rotational motion in a body.

(iv) Mechanical advantage greater than one means that small effort can be used to lift a large load.

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Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Centre of Mass

Two stars of masses

3 \times 10^{31} kg

each, and at distance

2 \times 10^{11} m

rotate in a plane about their common centre of mass

O .

A meteorite passes through

O

moving perpendicular to the star's rotation plane. In order to escape from the gravitational field of this double star, the minimum speed that meteorite should have at

O

is ( Take Gravitational constant

G = 6.67 \times 10^{- 11} N m^{2} {kg}^{- 2}

)

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Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Centre of Mass

A wheel of radius "rolls without slipping with a speed $v$ on a horizontal road. When it is at a point $A$ on the road a small bob of the mud separates from wheel at the highest point and touches the point $B$ on the road as shown in the figure. Then $A B$ is (g-acceleration due to gravity)

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Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Centre of Mass

A rigid ball rolls without slipping on a surface shown below.

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Which on the following is the most likely representation of the distance travelled by the ball vs time graph?

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Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Centre of Mass

On a pulley of mass $M$ hangs a rope with two masses $m_{1}$ and $m_{2} (m_{1} > m_{2})$ tied at the ends as shown in the figure. The pulley rotates without any friction, whereas the friction between the rope and the pulley is large enough to prevent any slipping. Which of the following plots best represents the difference between the tensions in the rope on the two sides of the pulley as a function of the mass of the pulley?

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What is called a rigid body?

Important Questions on Motion of System of Particles and Rigid Bodies

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