JEE Main · 2005 · 08 May 2005 · Offline · Rotational Mechanics

A 'T' shaped object with dimensions shown in the 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

(A) $\frac{2}{3} ℓ$
(B) $\frac{3}{2} ℓ$
(C) $\frac{4}{3} ℓ$ ✓ Correct
(D) $ℓ$

Answer: (C)

Solution

For the object to slide without turning, the applied force must pass through its centre of mass, so

P

must lie at the centre of mass measured from

C

. Treating the 'T' as the two rods shown and taking moments of their masses about

C

with the lengths marked in the figure, the mass-weighted mean position works out to

\frac{4 ℓ}{3}

from

C

. A force applied there has its line of action through the centre of mass, giving pure translation with no rotation.

JEE Main · 2005 · 08 May 2005 · Offline · Single correct option

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JEE Main · 2005 · 08 May 2005 · Offline · Rotational Mechanics

Solution

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