JEE Advanced · 2022 · 28 Aug 2022 · Paper 1 · Rotational Mechanics

A solid sphere of mass

1 k g

and radius

1 m

rolls without slipping on a fixed inclined plane with an angle of inclination

θ = 3 0^{\circ}

from the horizontal. Two forces of magnitude

1 N

each, parallel to the incline, act on the sphere, both at distance

r = 0.5 m

from the center of the sphere, as shown in the figure. The acceleration of the sphere down the plane is ____

m s^{- 2}

. (Take

g = 10 m s^{- 2}

Answer: 2.86

Solution

Forces along the incline:

m g sin 30° + 1 - 1 - f = ma

5 - f = a

Torque about center of mass:

f \times 1 - 2 (1 \times 0.5) = I α = \frac{2}{5} m r^{2} \times \frac{a}{r}

f - 1 = \frac{2}{5} a

f = 1 + \frac{2 a}{5}

Substituting:

5 - a = 1 + \frac{2 a}{5}

4 = \frac{7 a}{5}

a = \frac{20}{7} = 2.86 m / s^{2}

JEE Advanced · 2022 · 28 Aug 2022 · Paper 1 · Numerical answer

Practise more: all JEE Advanced PYQs on Rotational Mechanics →

More JEE Advanced questions on Rotational Mechanics

Consider a large disk of radius R and two smaller disks, each of radius $r = R /50$ , lying on its circumference, as shown in the figure. The smaller disks are initially in contact with each other, with an angular separation $Δ θ$ between their centers. …
JEE Advanced 2026View solution →
A solid cylinder of radius $R$ rolls without slipping with a center of mass speed $v_{0} = \frac{gR}{3}$ on a horizontal surface with a vertical edge, as shown in the figure. Here, $g$ is the acceleration due to the gravity. At the moment when the cylinder loses con …
JEE Advanced 2026View solution →
List-I shows four planar structures made of uniform solid rods each of mass $m$ and length $l$ . In the List-II the possible moment of inertia of these structures about an axis $OCO^{'}$ , which lies in the plane of the structures, are given.
Choose the option that de …
JEE Advanced 2026View solution →
A uniform circular disk of radius 0.2 m and mass 1 kg is pivoted at its top point $C$ such that it can rotate freely around $C$ in the $X Y$ plane, as shown in the figure. Initially, when the disk is at rest, a particle of mass 20 g, travelling along negative $x$ direction …
JEE Advanced 2026View solution →
A disc of mass $M$ and radius $R$ is free to rotate about its vertical axis as shown in the figure. A battery operated motor of negligible mass is fixed to this disc at a point on its circumference. Another disc of the same mass $M$ and radius $R /2$ is fixed to the moto …
JEE Advanced 2024View solution →
A thin uniform rod of length $L$ and certain mass is kept on a frictionless horizontal table with a massless string of length $L$ fixed to one end (top view is shown in the figure). The other end of the string is pivoted to a point O . If a horizontal impulse $P$ is imparte …
JEE Advanced 2024View solution →