(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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$0.7$
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$0.3$

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Newton's Laws of Motion and Friction

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Circular motion with Friction

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$A$ body of mass $M \text{ kg}$ is at the top point of a smooth hemisphere of radius $5 \text{ m}$. It is released to slide down the surface of the hemisphere. It leaves the surface when its velocity is $5 \text{ m/s}$. At this instant, the angle made by the radius vector of the body with the vertical is (Acceleration due to gravity $g = 10 \text{ m/s}^2$) (in $^{\circ}$)

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In a motorcycle stunt called the "well of death",the track is a vertical cylindrical surface of $18\, m$ diameter. What should be the minimum speed of the motorcyclist in $m/s$ to prevent him from sliding down? The coefficient of friction is $0.8$ and take $g = 10\, m/s^2$.

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$A$ circular racetrack of radius $300 \; m$ is banked at an angle of $15^{\circ}$. If the coefficient of friction between the wheels of a race-car and the road is $0.2$,what is the
$(a)$ optimum speed of the racecar to avoid wear and tear on its tyres,and
$(b)$ maximum permissible speed to avoid slipping?

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$A$ large drum having radius $R$ is spinning around its axis with angular velocity $\omega$, as shown in the figure. The minimum value of $\omega$ so that a body of mass $M$ remains stuck to the inner wall of the drum, taking the coefficient of friction between the drum surface and mass $M$ as $\mu$, is:

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$A$ car is moving along a circular path having a coefficient of friction $0.5$ and a radius of curvature $16.2 \,m$. The maximum velocity of the car that can travel without skidding outwards is (Acceleration due to gravity $= 10 \,ms^{-2}$)

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In a motorcycle stunt called the "well of death",the track is a vertical cylindrical surface of $18\, m$ diameter. What should be the minimum speed of the motorcyclist in $m/s$ to prevent him from sliding down? The coefficient of friction is $0.8$ and take $g = 10\, m/s^2$.

$A$ car is moving along a circular path having a coefficient of friction $0.5$ and a radius of curvature $16.2 \,m$. The maximum velocity of the car that can travel without skidding outwards is (Acceleration due to gravity $= 10 \,ms^{-2}$)

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