JEE Mains · Physics · STD 11 - 6. system of particles and rotational motion

To mop-clean a floor, a cleaning machine presses a circular mop of radius \(R\) vertically down with a total force \(F\) and rotates it with a constant angular speed about its axis. If the force \(F\) is distributed uniformly over the mop and the floor is \(\mu \), the torque, applied by the machine on the mop is

A \(\mu FR/3\)
B \(\mu FR/6\)
C \(\mu FR/2\)
D \(\frac{2}{3}\,\mu FR\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{2}{3}\,\mu FR\)

Step-by-step Solution

Detailed explanation

\(\begin{array}{l} d\tau = \left( {\mu dN} \right)x\\ \,\,\,\,\,\,\, = \mu \left( {\frac{F}{{\pi {R^2}}} \times 2\pi \times dx} \right)x\\ \,\,\,\,\tau = \int\limits_0^R {d\tau } \end{array}\)

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.

Same subject

Match List\(-I\) with List\(-II\).

List\(-I\)	List\(-II\)
\((a)\) \({R}_{{H}}\) (Rydberg constant)	\((i)\) \({kg} {m}^{-1} {s}^{-1}\)
\((b)\) \(h\) (Planck's constant)	\((ii)\) \({kg} {m}^{2} {s}^{-1}\)
\((c)\) \(\mu_{{B}}\) (Magnetic field energy density)	\((iii)\) \({m}^{-1}\)
\((d)\) \(\eta\) (coefficient of viscocity)	\((iv)\) \({kg} {m}^{-1} {s}^{-2}\)

Choose the most appropriate answer from the options given below:

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