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Hard Centre of mass of a two-particle system, centre of mass of a rigid body MCQs for JEE

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Part of Rotational Motion in JEE Main Physics.

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Q1PhysicsUnit 5: Rotational Motion
How far from the midpoint of the stick is the center of mass of the stick-puck combination after the collision?
Q2PhysicsUnit 5: Rotational Motion
Assertion The center of mass of a body may lie where there is no mass. Reason Centre of mass of a body is a point, where the whole mass of the body is supposed to be concentrated.
Q3PhysicsUnit 5: Rotational Motion
A uniform thin rod of length ll is standing on a smooth horizontal surface. A slight disturbance causes the lower end to slip to the smooth surface and the rod starts falling. Based on this information mark the correct option.
Q4PhysicsUnit 5: Rotational Motion
Particle 1 with mass MM has xx position defined by the function x1(t)=x_{1}(t)= 2t(t+3)2 t(t+3) where units are in meters time is in seconds, and are abbreviated in the function. Particle 2 has mass 2M2 M and xx position defined by x(t)=x(t)= (t−1)(t−2)/2(t-1)(t-2) / 2 Considering the system of these two particles, what is the velocity of the center of mass of the system at t=2?t=2 ?
Q5PhysicsUnit 5: Rotational Motion
Find the centre of mass of the letter FF which cut from a uniform metal sheet from point A\mathbf{A}
Q6PhysicsUnit 5: Rotational Motion
A stick is thrown in the air and lands on the ground at some distance from the thrower. The centre of mass of the stick will move along a parabolic path
Q7PhysicsUnit 5: Rotational Motion
At t=0,t=0, the position and velocities of two particle are as shown in the figure. They are kept on a smooth surface and being mutually attracted by gravitational force. Find the position of center of mass at t=2st=2 s
Q8PhysicsUnit 5: Rotational Motion
The motion of centre of mass depends on

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