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A torque of 0.5Nm is required to drive a screw into a wooden frame with the help of a screw driver. If one of the two forces of couple produced by screw driver is 50N, the width of the screw driver is:
A. 0.5cm
B. 0.75cm
C. 1cm
D. 1.5cm

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Last updated date: 18th Jun 2024
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Answer
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Hint:-We have been given two known variables: torque (0.5N) and force (50N) and an unknown variable: width of the driver. Apply the general formula for torque, here the radius is the width of the screw driver because the torque is acting along the width of the screw driver.
Formula Used: The formula for torque is given by:

$\tau = r \times F$;
Where:
$\tau = Torque$;
$r = {\text{ Radius / width of the screw driver}}$;
$F = Force$;

Complete step-by-step solution
Here apply the formula of torque and solve the unknown value that is the width of the screw driver:
$\tau = r \times F$;
Put the given value in the above equation;
$0.5 \times 100Ncm = r \times 50N$;
Keep the radius “r” on the RHS and take the other quantity to LHS,
$\dfrac{{0.5 \times 100}}{{50N}} = r$;
The value of r which is the width of the screw driver is:
$r = 1cm$;

Final Answer: Option “3” is correct. The width of the screw driver is 1cm.

Note:-
Torque is defined as the angular force required to rotate the object. Just like we have studied about the force F, the torque is just angular equivalent of the linear force. The formula$\tau = r \times F$ gives the relation between linear and angular force. The scalar version of the formula is $\tau = rF\sin \theta $. Where the angle plays an important role in determining the torque.