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Two forces 50N and 100 N are acting on a...

Two forces `50N and 100 N` are acting on a rod capable of rotating it about `O` as shown in Fig. What is the net torque acting on the rod ?

Text Solution

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In Fig. we have resolved force of `100 N` into two rectangular components : `100 cos 30^(@)` along the horizontal and `100 sin 30^(@)` along the vertical.
The horizontal component cannot rotate the rod.
Torque due to `F = 100 sin 30^(@)` about fixed `O`
`tau_(1) = 100 sin 30^(@) xx 0.5 = 100 xx (1)/(2) xx 0.5 = 25 Nm`
It is in clockwise direction.
Torque due to `F = 50N` about fixed point `O`
`tau_(2) = F xx 0.5 = 50 xx 0.5 = 25 Nm`
It is also clockwise.
`:.` Net torque acting on the rod `= tau_(1) + tau_(2) = 25 + 25 = 50Nm`, clockwise.
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Knowledge Check

  • Two forces F_(1) " and " F_(2) are acting on a rod abc as shown in figure.

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    C
    if `F_(1)neF_(2)` then `tau_(a)netau_(b)netau_(c)` ( for both forces)
    D
    if `F_(1)neF_(2)` then `tau_(a)=tau_(c)netau_(b)` ( for both forces)

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