MHT CET · Physics · Rotational Motion

A rod $l$ m long is acted upon by a couple as shown in the figure. The moment of couple is $τ$ Nm. If the force at each end of the rod, then magnitude of each force is
$(s i n 30^{o} = c o s 60^{o} = 0.5)$

A $\frac{τ}{l}$
B $\frac{l}{2 τ}$
C $\frac{2 τ}{l}$
D $\frac{2 l}{τ}$

Verified Solution

Answer & Solution

Correct Answer

(C) $\frac{2 τ}{l}$

Step-by-step Solution

Detailed explanation

Length of rod =

l

Moment of couple,

l τ = F l s i n θ

∴ F = \frac{τ}{l s i n θ} - \frac{τ}{l s i n 30^{o}} = \frac{τ}{l \times \frac{1}{2}}

Force,

F = \frac{2 τ}{l}

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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A rod l m long is acted upon by a couple as shown in the figure. The moment of couple is τ Nm. If the force at each end of the rod, then magnitude of each force is sin30o=cos60o=0.5

Step-by-step Solution

A rod $l$ m long is acted upon by a couple as shown in the figure. The moment of couple is $τ$ Nm. If the force at each end of the rod, then magnitude of each force is
$(s i n 30^{o} = c o s 60^{o} = 0.5)$