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The radius of gyration of a uniform disc about a line perpendicular to the disc equals its radius. The distance of the line from the centre is given as $\frac{r}{\sqrt{a}}$ . Find the value of $a$

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Important Questions on Rotational Mechanics

HARD

JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 1]>Chapter 10 - Rotational Mechanics>EXERCISES>Q 15

The moment of inertia of a uniform square plate of mass

m

and edge

a

about one of its diagonals is given as

\frac{m a^{2}}{β}

. Find the value of

β .

HARD

JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 1]>Chapter 10 - Rotational Mechanics>EXERCISES>Q 16

The surface density

(\frac{mass}{area})

of a circular disc of radius

a

depends on the distance from the centre as

ρ (r) = A + B r

. The moment of inertia about the line perpendicular to the plane of the disc through its centre is given by

2 π (\frac{A a^{4}}{α} + \frac{B a^{5}}{β})

. Find the value of

α + β .

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JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 1]>Chapter 10 - Rotational Mechanics>EXERCISES>Q 17

A particle of mass

m

is projected with a speed

u

at an angle

θ

with the horizontal. The torque of the weight of the particle is

{mu}^{x} \sin θ \cos θ

, which is perpendicular to the plane of motion. The value of

x

is:

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JEE Main

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CONCEPTS OF PHYSICS [VOLUME 1]>Chapter 10 - Rotational Mechanics>EXERCISES>Q 18

A simple pendulum of length

l

is pulled aside to make an angle

θ

with the vertical. The magnitude of the torque of the weight

w

of the bob about the point of suspension is

xsin θ

. The torque is zero when the bob is at the lowest point. The value of

x

is:

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JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 1]>Chapter 10 - Rotational Mechanics>EXERCISES>Q 19

When a force of $6.0 N$ is exerted at $30 °$ to a wrench at a distance of $8 cm$ from the nut, it is just able to loosen the nut. What force $F$ would be sufficient to loosen it if it acts perpendicularly to the wrench at $16 cm$ from the nut?

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JEE Main

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CONCEPTS OF PHYSICS [VOLUME 1]>Chapter 10 - Rotational Mechanics>EXERCISES>Q 20

Calculate the total torque acts on the body shown about the point $O$ .

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HARD

JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 1]>Chapter 10 - Rotational Mechanics>EXERCISES>Q 21

A cubical block of mass

m

and edge

a

slides down a rough inclined plane of inclination

θ

with uniform speed. The torque of the normal force acts on the block about its centre is

y mgasinθ

. The value of

y

is:

HARD

JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 1]>Chapter 10 - Rotational Mechanics>EXERCISES>Q 22

A rod of mass

m

and length

L

lying horizontally is free to rotate about a vertical axis through its centre. The horizontal force of constant magnitude

F

acts on the rod at a distance of

\frac{L}{4}

from the centre. The force is always perpendicular to the rod. The angle rotated by the rod during the time

t

after the motion starts is given as

\frac{α F t^{2}}{m L}

. Find the value of

α .

The radius of gyration of a uniform disc about a line perpendicular to the disc equals its radius. The distance of the line from the centre is given as ra. Find the value of a

Important Questions on Rotational Mechanics

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The radius of gyration of a uniform disc about a line perpendicular to the disc equals its radius. The distance of the line from the centre is given as $\frac{r}{\sqrt{a}}$ . Find the value of $a$