Question

Two boys are holding a horizontal rod of length $L$ and weight $W$ through its two ends. If now one of the boys suddenly leaves he rod. what is the instantaneous reaction force experienced by the other boy?

• A. $\frac{W}{4}$
• B. $\frac{W}{2}$
• C. $\frac{3W}{4}$
• D. $W$

Answer 1

Answer: (A)

$\frac{W}{4}$

Let 's consider,

$F=$ Force given by the boy

$W=$ weight

$L=$ length

$\alpha =$ angular acceleration

$a_{cm}=$ Linear acceleration of the center of the mass.

Linear equation of motion from the free body diagram

$W-F=\left(\frac{W}{g}\right)a_{cm}$. . . . . . . .(1)

We know that,

$W\left(\frac{L}{2}\right)=I\alpha$

$\frac{WL}{2}=\frac{W{L}^2}{3g}\alpha$ ($I=\frac{m{L}^2}{3},m=\frac{W}{g}$)

$\alpha =\frac{3g}{2L}$. . . . . .(2)

The acceleration of center of mass

$a_{cm}=\frac{\alpha L}{2}=\frac{3g}{4}$

Substitute in equation (1), we get,

$W-F=\frac{W}{g}\times \frac{3g}{4}$

$F=W-\frac{3W}{4}=\frac{4W-3W}{4}$

$F=\frac{W}{4}$

The correct option is A.