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Q.

A solid cylinder of mass m = 6 kg and radius r = 0.1 m kept in balance on a slope of inclination α = 37° with the help of a thread fastened to its jacket. The cylinder does not slip on the slope. The minimum required coefficient of friction to keep the cylinder in balance when the thread is held vertically is $\frac{n}{100}$ Find the value of n = _____

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answer is 75.

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Detailed Solution

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$N + \frac{4 F}{5} = \frac{4}{5} mg \Rightarrow N = \frac{4}{5} mg - \frac{4}{5} F$

$f = μ (\frac{4 mg}{5} - \frac{4 F}{5}) . . . (1)$

$f + \frac{3 F}{5} = \frac{3}{5} mg \dots (2)$

from rotational equilibrium,

$fr = F \times r \Rightarrow f = F . . . (3)$

Solving equation (1) , (3)

$μ = \frac{3}{4} (or) \frac{75}{100}$

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A solid cylinder of mass m = 6 kg and radius r = 0.1 m kept in balance on a slope of inclination α = 37° with the help of a thread fastened to its jacket. The cylinder does not slip on the slope. The minimum required coefficient of friction to keep the cylinder in balance when the thread is held vertically is n100Find the value of n = _____