A rectangular slab A B C D has dimensions a × 2 a as shown in figure. Match the following two columns. Column I Column II (i) Radius of gyration about axis- 1 (P) a 12 (ii) Radius of gyration about axis- 2 (Q) 2 a 3 (iii) Radius of gyration about axis- 3 (R) a 3 (iv) Radius of gyration about axis- 4 (S) None

i - b i i - c i i i - c i v - a

i - b i i - a i i i - c i v - c

i - d i i - b i i i - a i v - c

i - c i i - a i i i - d i v - b

Square frame is made of four uniform rods. Mass of each rod is m and length l . Match column I with column II. Column I (Axis of rotation) Column II (Moment of inertia about axis of rotation) (i) (a) 2 3 m l 2 (ii) (b) 5 3 m l 2 (iii) (c) 7 3 m l 2 (iv) (d) 8 3 m l 2

i - d i i - b i i i - a i v - c

i - b i i - a i i i - c i v - c

i - b i i - a i i i - d i v - c

i - c i i - a i i i - d i v - b

For the situations given in column I match the corresponding values of moment of inertia about an axis passing through O . Column I (Axis of rotation) Column II (Moment of inertia about axis of rotation) (i) A rod of mass m length 3 l is bent at O . (a) 7 3 m l 2 (ii) L -shaped composite rod comprising two identical rods, each of mass m and length l . (b) 17 12 m l 2 (iii) A rod of mass m and length l is rotating about an axis passing through O . (c) m l 2 (iv) Two identical rods, each of mass m and length l , are welded as shown. (d) 55 48 m l 2

i - c i i - a i i i - d i v - b

i - b i i - a i i i - c i v - c

i - b i i - a i i i - d i v - c

i - d i i - b i i i - a i v - c

EASY

JEE Advanced

IMPORTANT

Earn 100

A hexagonal body lies on a horizontal rough surface. A force $F$ acts on the side of a hexagonal body as shown in figure. Choose the correct option(s).

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Important Questions on Rigid Body Dynamics: Part 1

MEDIUM

JEE Advanced

IMPORTANT

Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 3 - Rigid Body Dynamics: Part 1>Exercises>Q 17

A stick

A B

of mass

M

is tied at one end to a light string

O A

. A horizontal force

F = M g

is applied at end

B

of the stick and it remains in equilibrium in position shown. Then,
Question Image

EASY

JEE Advanced

IMPORTANT

Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 3 - Rigid Body Dynamics: Part 1>Exercises>Q 5

A rectangular slab

A B C D

has dimensions

a \times 2 a

as shown in figure. Match the following two columns.
Question Image

	Column I		Column II
(i)	Radius of gyration about axis- $1$	(P)	$\frac{a}{\sqrt{12}}$
(ii)	Radius of gyration about axis- $2$	(Q)	$\frac{2 a}{\sqrt{3}}$
(iii)	Radius of gyration about axis- $3$	(R)	$\frac{a}{\sqrt{3}}$
(iv)	Radius of gyration about axis- $4$	(S)	None

EASY

JEE Advanced

IMPORTANT

Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 3 - Rigid Body Dynamics: Part 1>Exercises>Q 6

A body of radius

r

rolls without sliding on a curved surface of radius of curvature

R

as shown in the figure. Match the Columns:
Question Image

	Column I		Column II
(i)	$ω_{C O}$	(a)	$\frac{v}{r}$
(ii)	$ω_{C P}$	(b)	$\frac{v}{R - r}$
(iii)	$ω_{P C}$	(c)	$\frac{a}{R - r}$
(iv)	$α_{C O}$	(d)	$\frac{a}{r}$

HARD

JEE Advanced

IMPORTANT

Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 3 - Rigid Body Dynamics: Part 1>Exercises>Q 7

Square frame is made of four uniform rods. Mass of each rod is

m

and length

l

. Match column I with column II.

		Column II (Moment of inertia about axis of rotation)
(i)	(a)	$\frac{2}{3} m l^{2}$
(ii)	(b)	$\frac{5}{3} m l^{2}$
(iii)	(c)	$\frac{7}{3} m l^{2}$
(iv)	(d)	$\frac{8}{3} m l^{2}$

MEDIUM

JEE Advanced

IMPORTANT

Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 3 - Rigid Body Dynamics: Part 1>Exercises>Q 8

A disc rolls on ground without slipping. The velocity of centre of mass is

v

. There is a point

P

on circumference of disc at angle

θ

. Suppose

v_{p}

is the speed of this point. Then, match the following:
Question Image

	Column I		Column II
(i)	$I f θ = 60^{o}$ ,	(a)	$v_{p} = \sqrt{2} v$
(ii)	$I f θ = 90^{o}$ ,	(b)	$v_{p} = v$
(ii)	$If θ = 120^{o}$ ,	(c)	$v_{p} = 2 v$
(iv)	$I f θ = 18^{o}$ ,	(d)	$v_{p} = \sqrt{3} v$

HARD

JEE Advanced

IMPORTANT

Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 3 - Rigid Body Dynamics: Part 1>Exercises>Q 10

For the situations given in column I match the corresponding values of moment of inertia about an axis passing through

O

	Column I (Axis of rotation)		Column II (Moment of inertia about axis of rotation)
(i)	A rod of mass $m$ length $3 l$ is bent at $O$ .	(a)	$\frac{7}{3} m l^{2}$
(ii)	$L$ -shaped composite rod comprising two identical rods, each of mass $m$ and length $l$ .	(b)	$\frac{17}{12} m l^{2}$
(iii)	A rod of mass $m$ and length $l$ is rotating about an axis passing through $O$ .	(c)	$m l^{2}$
(iv)	Two identical rods, each of mass $m$ and length $l$ , are welded as shown.	(d)	$\frac{55}{48} m l^{2}$

HARD

JEE Advanced

IMPORTANT

Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 3 - Rigid Body Dynamics: Part 1>Exercises>Q 1

A solid cylinder with $r = 0.1 m$ and mass $M = 2 kg$ is placed such that it is in contact with the vertical and a horizontal surface as shown in figure. The coefficient of static friction is $μ = (1 / 3)$ for both the surfaces. Find the distance $d$ (in $cm$ ) from the centre of the cylinder at which a force $F = 40 N$ should be applied vertically so that the cylinder just starts rotating in anticlockwise direction.

Question Image

HARD

JEE Advanced

IMPORTANT

Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 3 - Rigid Body Dynamics: Part 1>Exercises>Q 2

A uniform rod $A B$ of mass $2 kg$ is hinged at one end $A .$ The rod is kept in the horizontal position by a massless string tied to point $B .$ Find the reaction of the hinge (in $N$ ) on end $A$ of the rod at the instant when string is cut. $(g = 10 m / s^{2})$

Question Image

A hexagonal body lies on a horizontal rough surface. A force F acts on the side of a hexagonal body as shown in figure. Choose the correct option(s).

Important Questions on Rigid Body Dynamics: Part 1

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A hexagonal body lies on a horizontal rough surface. A force $F$ acts on the side of a hexagonal body as shown in figure. Choose the correct option(s).