Centre of Mass

Statement-1 : The centre of mass and centre of gravity of a body are two different positions in general. and Statement-2 : The centre of mass and centre of gravity of a body coincide if graviational field is unifrom.

Considering a system having two masses m_(1) and m_(2) in which first mass is pushed towards centre of mass by a distance a, the distance required to be moved for second mass to keep centre of mass at same position is :-

As the temperature is increased, the period of a pendulum a) Increases as its effective length increases even through its centre of mass still remains at the centre of the bob. b) decreases as its effective length increases even though its centre of mass still remains at the centre of the bob. c) Increases as its effective length increases due to shifting of centre of mass below the centre of the bob. d) decreases as its effective length remains same but the centre of mass shifts above the centre of the bob.

If net force on a system of particles is zero. Then {:(,"Column I",,"Column II",),((A),"Acceleration of centre of mass",(p),"Constant",),((B),"Velocity of centre of mass",(q),"Zero",),((C ),"Momentum of centre of mass",(r ),"May be zero",),((D),"Velocity of an individual particle of the system",(s),"May be constant",):}

A uniform circular disc of mass M and radius R is pivoted at distance x above the centre of mass of the disc, such that the time period of the disc in the vertical plane is infinite. What is the distance between the pivoted point and centre of mass of the disc ?

The mass of a body cannot be considered to be concentrated at the centre of mass of the body for the purpose of computing its moment of inertia. For then the moment of inertia of every body about an axis passing through its centre of mass would be zero.

STATEMENT-1 : The relation vectau=(dvecL)/(dt) is applicable in centre of mass frame, even though the centre of mass is accelerating. and STATEMENT-2 : The relation vectau=(dvecL)/(dt) can be directly applied in a non-inertial frame.

Assertion: A constant force F is applied on two blocks and one spring system as shown in figure. Velocity of centre of mass increases linearly with time. Reason: Acceleration of centre of mass is constant.

In a double star system one of mass m_(1) and another of mass m_(2) with a separation d rotate about their common centre of mass. Then rate of sweeps of area of star of mass m_(1) to star of mass m_(2) about their common centre of mass is

Two identical uniform rods AB and CD, each of length L are jointed to form a T-shaped frame as shown in figure. Locate the centre of mass of the frame. The centre of mass of a uniform rod is at the middle point of the rod.