A T-shaped object of uniform thickness and sa | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) For an object to undergo pure translational motion,the net force must be applied at its centre of mass $(CM)$.Let the horizontal bar $AB$ have mas

Vedclass · Accepted Answer

$\frac {4l}{3}$

Vedclass · Answer

(A) For an object to undergo pure translational motion,the net force must be applied at its centre of mass $(CM)$.Let the horizontal bar $AB$ have mass $m$ and the vertical bar have mass $2m$ (since its length is $2l$ compared to $l$ for $AB$).Let the junction of the two bars be the origin $(0,0)$.The centre of mass of the horizontal bar is at $(0,0)$.The centre of mass of the vertical bar is at $(0, -l)$.The total mass of the object is $M = m + 2m = 3m$.The $y$-coordinate of the centre of mass is given by:$Y_{CM} = \frac{m(0) + 2m(-l)}{3m} = \frac{-2ml}{3m} = -\frac{2l}{3}$.This means the centre of mass is at a distance of $\frac{2l}{3}$ from the junction towards $C$.Since the total length of the vertical bar is $2l$,the distance of the centre of mass from $C$ is $2l - \frac{2l}{3} = \frac{4l}{3}$.

Similar Questions

The centre of mass of two particles lies:

For a system consisting of two objects,when can they be treated as point particles?

Masses $m \left(\frac{1}{3}\right)^N \frac{1}{N}$ are placed at $x=N$,where $N=2, 3, 4, \ldots \infty$. If the total mass of the system is $M$,then the centre of mass is

Infinite numbers of blocks are placed on a table edge as shown in the diagram. What is the minimum value of $L$ so that the blocks are just going to topple over the table?

Two objects of masses $200 \text{ g}$ and $500 \text{ g}$ possess velocities $10 \hat{i} \text{ m/s}$ and $(3 \hat{i} + 5 \hat{j}) \text{ m/s}$ respectively. The velocity of their centre of mass in $\text{m/s}$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module