Center of Mass and System of Particles

A disc of radius 20 cm has its center at origin. If a disc of radius 5 cm is cut from it such that its edge touches the edge of the bigger disc, find the location of centre of mass of the new system.

(Shift I Memory Based)

A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of \(2: 1\). After disintegration they will move :

[JEE Main 2024, 09 Apr (Shift 2)]

A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of \(2: 1\). After disintegration they will move :

[JEE Main 2024, 09 Apr (Shift 2)]

Consider a circular disc of radius 20 cm with centre located at the origin. A circular hole of radius 5 cm is cut from this disc in such a way that the edge of the hole touches the edge of the disc. The distance of centre of mass of residual or remaining disc from the origin will be:

[JEE Main 2025, 23 Jan (Shift 1)]

Consider a circular disc of radius 20 cm with centre located at the origin. A circular hole of radius 5 cm is cut from this disc in such a way that the edge of the hole touches the edge of the disc. The distance of centre of mass of residual or remaining disc from the origin will be

[JEE Main 2025, 23 Jan (Shift 1)]

Consider a circular disc of radius 20 cm with centre located at the origin. A circular hole of radius 5 cm is cut from this disc in such a way that the edge of the hole touches the edge of the disc. The distance of centre of mass of residual or remaining disc from the origin will be:

A disc of radius 20 cm has its center at origin. If a disc of radius 5 cm is cut from it such that its edge touches the edge of the bigger disc, find the location of centre of mass of the new system.

(Shift I Memory Based)

A block moving horizontally on a smooth surface with a speed of 40 m/s splits into two parts with masses in the ratio of \(1:2\). If the smaller part moves at 60 m/s in the same direction, then the fractional change in kinetic energy is:

[JEE Main 2021, 31 Aug (Shift 2)]

A projectile is thrown from a point \(\mathrm{O}\) on the ground at an angle \(45^{\circ}\) from the vertical and with a speed \(5 \sqrt{2} \mathrm{~m} / \mathrm{s}\). The projectile at the highest point of its trajectory splits into two equal parts. One part falls vertically down to the ground, \(0.5 \mathrm{~s}\) after the splitting. The other part, \(t\) seconds after the splitting, falls to the ground at a distance \(x\) meters from the point \(O\). The acceleration due to gravity \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\).The value of t is ___.

[JEE Advanced 2021]

A rubber ball is released from a height of \( 5 \mathrm{~m} \) above the floor. It bounces back repeatedly, always rising to \( \frac{81}{100} \) of the height through which it falls. Find the average speed of the ball. (Take \( \mathrm{g}=10 \mathrm{~ms}^{-2} \) )

[JEE Main 2021, 17 Mar (Shift 2)]

A rubber ball is released from a height of \( 5 \mathrm{~m} \) above the floor. It bounces back repeatedly, always rising to \( \frac{81}{100} \) of the height through which it falls. Find the average speed of the ball. (Take \( \mathrm{g}=10 \mathrm{~ms}^{-2} \) )