(C) For the block to remain stationary,the upward frictional force must balance the downward gravitational force.$f_s = mg$The normal force $N$ provid

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(C) For the block to remain stationary,the upward frictional force must balance the downward gravitational force.$f_s = mg$The normal force $N$ provided by the wall acts as the centripetal force for the block's circular motion:$N = mr\omega^2$The maximum static frictional force is given by:$f_{L} = \mu N = \mu mr\omega^2$For the block to stay in equilibrium,the frictional force must be at least equal to the weight:$f_{L} \geq mg$$\mu mr\omega^2 \geq mg$Solving for $\omega$:$\omega^2 \geq \frac{g}{\mu r}$$\omega \geq \sqrt{\frac{g}{\mu r}}$Substituting the given values ($g = 10\; m/s^2$,$\mu = 0.1$,$r = 1\; m$):$\omega_{\min} = \sqrt{\frac{10}{0.1 \times 1}} = \sqrt{\frac{10}{0.1}} = \sqrt{100} = 10\; rad/s$

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

Medium

$A$ block of mass $10\; kg$ is in contact with the inner wall of a hollow cylindrical drum of radius $1\; m$. The coefficient of friction between the block and the inner wall of the cylinder is $0.1$. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis will be: ......$rad/s$ $(g = 10\; m/s^2)$

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A
$\sqrt{10}$
B
$\frac{10}{2\pi}$
C
$10$
D
$10\pi$

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Class 11

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Newton's Laws of Motion and Friction

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Circular motion with Friction

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$A$ bead of mass $m$ stays at point $P(a, b)$ on a wire bent in the shape of a parabola $y = 4Cx^2$ and rotating with angular speed $\omega$ (see figure). The value of $\omega$ is (neglect friction).

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$A$ van is moving with a speed of $108 \,km/hr$ on a level road where the coefficient of friction between the tyres and the road is $0.5$. For the safe driving of the van, the minimum radius of curvature of the road shall be (Acceleration due to gravity, $g = 10 \,m/s^2$) (in $\,m$)

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$A$ modern grand-prix racing car of mass $m$ is travelling on a flat track in a circular arc of radius $R$ with a speed $v$. If the coefficient of static friction between the tyres and the track is $\mu_{s},$ then the magnitude of negative lift $F_{L}$ acting downwards on the car is (Assume forces on the four tyres are identical and $g =$ acceleration due to gravity)

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$A$ $100 \, kg$ car is moving with a maximum velocity of $9 \, m/s$ across a circular track of radius $30 \, m$. The maximum force of friction between the road and the car is ........ $N$.

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$A$ $70 \; kg$ man stands in contact against the inner wall of a hollow cylindrical drum of radius $3 \; m$ rotating about its vertical axis. The coefficient of friction between the wall and his clothing is $0.15$. What is the minimum rotational speed (in $rad/s$) of the cylinder to enable the man to remain stuck to the wall (without falling) when the floor is suddenly removed? (Take $g = 10 \; m/s^2$)

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$A$ bead of mass $m$ stays at point $P(a, b)$ on a wire bent in the shape of a parabola $y = 4Cx^2$ and rotating with angular speed $\omega$ (see figure). The value of $\omega$ is (neglect friction).

$A$ van is moving with a speed of $108 \,km/hr$ on a level road where the coefficient of friction between the tyres and the road is $0.5$. For the safe driving of the van, the minimum radius of curvature of the road shall be (Acceleration due to gravity, $g = 10 \,m/s^2$) (in $\,m$)

$A$ $100 \, kg$ car is moving with a maximum velocity of $9 \, m/s$ across a circular track of radius $30 \, m$. The maximum force of friction between the road and the car is ........ $N$.

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