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Standard XII

Mathematics

Definition of Vector

A force is ap...

Question

A force is applied to the end of a $2 m$ long uniform board weighing $50 N$ in order to keep it horizontal, while it pushes against a wall at the left. If the angle the force makes with the board is $30$ in the direction shown, the applied force $F$ is:

25 N

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43.3 N

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50 N

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100 N

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Solution

The correct option is C $50 N$
R.E.F image
Since $W$ is trying to rotate it in clockwise direction
$F sin 30$ will balance it out
$\Rightarrow τ = r \times F$
$w \times (1 m) = F sin 30 \times (2 m)$
$50 \times 1 = F \times \frac{1}{2} \times 2$
$\Rightarrow F = 50 N$

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A force is applied to the end of a 2 m long uniform board weighing 50 N in order to keep it horizontal, while it pushes against a wall at the left. If the angle the force makes with the board is 30 in the direction shown, the applied force F is:

The correct option is C 50 NR.E.F imageSince W is trying to rotate it in clockwise direction Fsin30 will balance it out ⇒τ=r×Fw×(1m)=Fsin30×(2m)50×1=F×12×2⇒F=50N

A force is applied to the end of a $2 m$ long uniform board weighing $50 N$ in order to keep it horizontal, while it pushes against a wall at the left. If the angle the force makes with the board is $30$ in the direction shown, the applied force $F$ is:

The correct option is C $50 N$
R.E.F image
Since $W$ is trying to rotate it in clockwise direction
$F sin 30$ will balance it out
$\Rightarrow τ = r \times F$
$w \times (1 m) = F sin 30 \times (2 m)$
$50 \times 1 = F \times \frac{1}{2} \times 2$
$\Rightarrow F = 50 N$