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Center of Mass as an Average Point

A rigid massl...

Question

A rigid massless rod $A B$ of length $1 m$ is placed horizontally on two rigid supports at its ends as shown in figure. A weight $10 N$ is hung from a point $C$ at a distance $30 c m$ from $A$ . Find the reactions at the supports $A$ and $B$ respectively.

5 N, 5 N

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3 N, 7 N

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10 N, 0 N

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7 N, 3 N

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Solution

The correct option is D $7 N, 3 N$
$10 N$ force is acting downwards. Let the reaction force on $A$ and $B$ be $R_{a}$ and $R_{b}$ respectively which are acting upwards.
Now, since the whole system is in equilibrium.
Moment of forces about point $A$ , i.e., $M_{A} = 0,$ or, $- 10 \times 0.3) + R_{b} \times 1 = 0$ or, $R_{b} = 3 N$
Summation of all vertical forces is zero, i.e., $R_{a} - 10 + R_{b} = 0$
or, $R_{a} = 10 - 3 = 7 N$
So option $(4)$ is correct

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A rigid massless rod AB of length 1m is placed horizontally on two rigid supports at its ends as shown in figure. A weight 10N is hung from a point C at a distance 30cm from A. Find the reactions at the supports A and B respectively.

A rigid massless rod $A B$ of length $1 m$ is placed horizontally on two rigid supports at its ends as shown in figure. A weight $10 N$ is hung from a point $C$ at a distance $30 c m$ from $A$ . Find the reactions at the supports $A$ and $B$ respectively.