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 :

Question

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) (2/3) l (B) (3/2) l (C) (4/3) l (D) l

Tardigrade Admin · Accepted Answer

For pure translatory motion, net torque about centre of mass should be zero.
Thus,

F

is applied at centre of mass of system.

OP = \frac{m _{1} \times O + m _{1} \times l}{m _{1} + m _{2}}

where,

m_{1}

and

m_{2}

are masses of horizontal and vertical section of the object. Assuming object is uniform,

m_{2} = 2 m_{1} \Rightarrow OP = \frac{2 l}{3}

∴ PC = (l - \frac{2 l}{3} + l)

= (2 l - \frac{2 l}{3}) = \frac{4 l}{3}

Q. 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 $A B$ , such that the object has only the translational motion without rotation. Find the location of $P$ with respect to $C$ :

$\frac{2}{3} l$

$\frac{3}{2} l$

$\frac{4}{3} l$

$l$

Q. 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 :

32​l

23​l

34​l

l

Q. 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 $A B$ , such that the object has only the translational motion without rotation. Find the location of $P$ with respect to $C$ :

$\frac{2}{3} l$

$\frac{3}{2} l$

$\frac{4}{3} l$

$l$