A solid sphere with uniform density and radius R is rotating… | JEE Main 2025 (4 Apr, Shift 2)

Q19JEE Main 2025 · 4 APR · SHIFT 2Medium

Angular Momentum & its Conservation

A solid sphere with uniform density and radius $R$ is rotating initially with constant angular velocity $(\omega_1)$ about its diameter. After some time during the rotation it starts losing mass at a uniform rate, with no change in its shape. The angular velocity of the sphere when its radius become $R/2$ is $x\omega_1$ . The value of $x$ is _________.

Numerical answer type. Work it out, then open the answer.

Show answer and solution

Answer: 32

Density and shape unchanged, so $M\propto R^3$ : at $R/2$ , mass is $M/8$ .
$I=\frac25MR^2\propto R^5\Rightarrow I'=\frac{I}{32}$
Taking angular momentum conserved: $I\omega_1=\frac{I}{32}\omega$
$\omega=32\omega_1$ , so $x=32$ .

Report a mistake

More questions on Angular Momentum & its Conservation

Two discs of moment of inertia ' I₁ ' and ' I₂ ' and angular speeds ' ω₁ ' and ' ω₂ ' are…MHT CET 2025 (25 Apr, Shift 1)
The position vectors of two 1 kg particles, (A) and (B), are given by rA = (α₁ t²i + α₂…JEE Main 2025 (22 Jan, Shift 1)
The earth is assumed to be a sphere of radius ' R ' and mass ' M ' having period of…MHT CET 2024 (3 May, Shift 2)
A particle of mass ' m ' is rotating in a circular path of radius ' r '. Its angular…MHT CET 2024 (9 May, Shift 2)
A particle of mass m is projected with a velocity ' u ' making an angle of 30° with the…JEE Main 2024 (30 Jan, Shift 1)
A body of mass ' m ' is projected with a speed ' u ' making an angle of 45° with the…JEE Main 2024 (31 Jan, Shift 2)
A body of mass 5 kg moving with a uniform speed 3√(2) ms⁻¹ in X - Y plane along the line…JEE Main 2024 (29 Jan, Shift 2)
A circular table is rotating with an angular velocity of ω rad/s about its axis (see…JEE Main 2024 (8 Apr, Shift 2)

Angular Momentum & its Conservation question from JEE Main 2025 (4 Apr, Shift 2)

More questions on Angular Momentum & its Conservation