Question 30: Centre of Mass and Rotational Motion

Question

A T-shaped object with dimensions shown in figure, is lying on a smooth floor. A force F is applied at the point P parallel to AB, such that the object has only the translational motion without rotation. Find the location of P with respect to C.

Accepted Answer

Let O be the centre of mass of part AB and Q that of CD. Let M be the mass per unit length of the parts AB and CD.
As, no rotation is set up about point P, so
moment of part AB about P = moment of part CD about P
or, (ml) x = (2 ml) (I $$-$$ x) [$$\because$$ $$m = {M \over I}$$]
or, x = 2I $$-$$ 2x
or, x = 2I / 3
Distance of P from the end C = 2I $$-$$ 2I/3 = 4I/3

Answer

$${2 \over 3}I$$

Answer

$${3 \over 4}I$$

Answer

$${3 \over 2}I$$

Answer

$${4 \over 3}I$$

Centre of Mass and Rotational Motion

A T-shaped object with dimensions shown in figure, is lying on a smooth floor. A force F is applied at the point P parallel to AB, such that the object has only the translational motion without rotation. Find the location of P with respect to C.

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