An elastic rod, 30 cm long, of negligible weight, hangs downwards

| An elastic rod, 30 cm long, of negligible weight, hangs downwards from support. In one case load is applied on rod 20 cm below the support and in the other case the same load is applied at bottom of the rod. The reactions at supports will be

A. More in first case

B. Same in both the cases

C. More in second case

D. None of the above

Please scroll down to see the correct answer and solution guide.

Right Answer is: B

SOLUTION

Explanation:

The reaction at support can be found by using the equilibrium equation in static loading conditions. These equations are;

(i) Σ F_x = 0 (Summation of all forces in x-direction)

(ii) Σ F_y = 0 (Summation of all forces in y-direction)

(iii) Σ M = 0 (Summation of all the moments)

For the first case when the load is applied at 20 cm below the support, let reaction at support is R₁

From, Σ Fy = 0

R₁ = Load applied (P)

For the second case when the load is applied at the bottom of the rod, let reaction at support is R₂

From, Σ Fy = 0

R₂ = Load applied(P)

Hence in both the cases reaction at the support will be same which is equal to the load applied on the rod.

For of vertically hanging bar/rod supported at one end, the support reaction is independent of the distance of point of application of load from support.