1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# A uniform ′T′ shaped object with dimensions as shown in the figure, is lying on a smooth floor. A force →F is applied at the point P parallel to limb AB, such that the object has only the translational motion without rotation. Find the distance of point P from C

A
2l3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
3l2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
4l3
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
l
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is C 4l3→F must be directed towards the centre of mass of system, so that it passes through COM and →τext=0 ⇒ If τext=0 then angular acceleration of body α=0, which means that rotational aspect of motion will be absent, and body will be in pure translational motion. ∵ T shape is symmetrical about y− axis hence, COM will lie along y− axis only. Considering origin O at the centre of horizontal limb of length l and axis as shown in figure: since (length ∝ mass), for uniform rod ∴ m1=m, m2=2m m2→vertical limb of length 2l Replacing the individual limbs with a point mass placed at their respective COM: y1=0, y2=l ⇒yCM=m1y1+m2y2m1+m2 yCM=(m×0)+(2m×l)m+2m=2ml3m ∴yCM=2l3 ⇒PC=CO−PO=(2l−2l3) Distance of point P with respect to C, ∴PC=4l3

Suggest Corrections
69
Join BYJU'S Learning Program
Explore more
Join BYJU'S Learning Program