Question

A uniform beam of weight W is support horizontally by means of supports A and B at its ends. Find the reaction at A immediately after B is withdrawn.

• A. W/4
• B. 3W/4
• C. W/2
• D. W

Answer 1

Answer: (A)

W/4

Answer 2

When the support ‘B’ is withdrawn, the beam starts turning about A. Angular acceleration of beam about A, when B is withdrawn

α = $\frac{\frac{WL}{2}}{I} = \frac{\frac{WL}{2}}{\frac{WL^{2}}{3g}} = \frac{3g}{2L}\frac{L}{2}$ = $\frac{3g}{4}$

Now, W − R = $\frac{W}{g}$a_t

W − R = $\frac{3g}{4}$×$\frac{W}{g}$

W − R = $\frac{3W}{4}$ ⇒ R = W/4

Hence, (1) is correct.