Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
99 Percentile Qs Bank for JEE MainPhysicsCenter of Mass, Momentum and Collision

In the figure shown a semicircular area is removed from a uniform square plate of side l and mass (before removing) m . The x - coordinate of centre of mass of remaining portion is (The origin is at the centre of square)

Options

  1. A- π ( π - 2 ) ℓ 2 ( 8 - π )
  2. Bπ ( π - 2 ) ℓ 2 ( 8 - π )
  3. C- π π - 2 ℓ 8 - π
  4. DNone of these

Correct answer

D. None of these

Step-by-step solution

The centre of mass about x - axis is given as, x cm = m 1 x 1 + m 2 x 2   m 1 + m 2 Here, m 1 = mass of the square plate = m x 1 = centre of mass of the square plate = 0 (As the origin is at centre of the square) m 2 = mass of the removed part = mass density of square × area of the semicircular = - m l 2 π l 2 2 2 = - π 8 m x 2 = centre of mass of the removed part = l 2 - 4 3 π l 2 = l 2 1 - 4 3 π Now, the centre of mass of the system will be, x cm = - π m 8 × l 2 1 - 4 3 &#9

Practice Center of Mass, Momentum and Collision on Quantrex Academy →

More from Center of Mass, Momentum and Collision

Two identical bodies A and B of equal masses have initial velocities v₁ = 4 i m/s and v₂ = 4 j m/s respectively. The body A has acceleration a₁ = 6 i + 6 j m/s ^2 while the acceler 2026The position of center of mass of three masses 2 kg, 3 kg and 15 kg placed with respect to mid point ( p ) of normal bisector, as shown in the figure is _______. 2026Two blocks of masses 2 kg and 1 kg respectively, are tied to the ends of a string which passes over a light frictionless pulley as shown in the figure below. The masses are held at 2026The position of an object having mass 0.1 kg as a function of time t is given as r = (10t^2 i + 5t^3 j ) m. At t = 1 s, which of the following statements are correct ? A. The linea 2026A body of mass 14 kg initially at rest explodes and breaks into three fragments of masses in the ratio 2: 2: 3 . The two pieces of equal masses fly off perpendicular to each other 2026In a perfectly inelastic collision, two spheres made of the same material with masses 15 kg and 25 kg, moving in opposite directions with speeds of 10 ~m / s and 30 ~m / s , respec 2026Given below are two statements : Statement I : For a mechanical system of many particles total kinetic energy is the sum of kinetic energies of all the particles. Statement II : Th 2026In a scattering experiment, a particle of mass 2 m collides with another particle of mass m , which is initially at rest. Assuming the collision to be perfectly elastic, the maximu 2025 Full Center of Mass, Momentum and Collision list All 99 Percentile Qs Bank for JEE Main PYQs