(A) For the mass to remain stuck to the wall, the force of static friction $(f)$ must balance the gravitational force $(mg)$: $f = mg$.Since $f = \mu

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(A) For the mass to remain stuck to the wall, the force of static friction $(f)$ must balance the gravitational force $(mg)$: $f = mg$.Since $f = \mu N$, where $N$ is the normal force, we have $\mu N = mg$.The normal force is provided by the centripetal force: $N = m\omega^2R$.Substituting $N$ into the friction equation: $\mu (m\omega^2R) = mg$.Solving for $\mu$: $\mu = \frac{g}{\omega^2R}$.Given $g = 10 \ m/s^2$, $\omega = 5 \ rad/s$, and $R = 4 \ m$:$\mu = \frac{10}{5^2 \times 4} = \frac{10}{25 \times 4} = \frac{10}{100} = 0.1$.

Class 11 Physics Newton's Laws of Motion and Friction Circular motion with Friction

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$A$ $0.5 \ kg$ mass is in contact against the inner wall of a cylindrical drum of radius $4 \ m$ rotating about its vertical axis. The minimum rotational speed of the drum to enable the mass to remain stuck to the wall (without falling) is $5 \ rad/s$. The coefficient of friction between the drum's inner wall surface and mass is . . . . . . . (Take $g = 10 \ m/s^2$)

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$0.1$
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$0.5$
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$0.7$
D
$0.3$

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Newton's Laws of Motion and Friction

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Circular motion with Friction

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$A$ train runs along an unbanked circular track of radius $30 \; m$ at a speed of $54 \; km/h$. The mass of the train is $10^{6} \; kg$. What provides the centripetal force required for this purpose - the engine or the rails? What is the angle of banking required to prevent wearing out of the rail?

$A$ boy is sitting on the horizontal platform of a joy wheel at a distance of $5 \, m$ from the center. The wheel begins to rotate and when the angular speed exceeds $1 \, rad/s$,the boy just slips. Find the coefficient of friction between the boy and the wheel. (Take $g = 10 \, m/s^2$)

$A$ car moves along a circular track of radius $R$ banked at an angle of $30^o$ to the horizontal. The coefficient of static friction between the wheels and the track is $\mu$. The maximum speed with which the car can move without skidding out is

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