(D) The mass slides off when the centripetal force required exceeds the maximum static frictional force.$\frac{mv^2}{R} = \mu mg$$v = \sqrt{\mu Rg}$On

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(D) The mass slides off when the centripetal force required exceeds the maximum static frictional force.$\frac{mv^2}{R} = \mu mg$$v = \sqrt{\mu Rg}$Once the mass leaves the disc,it undergoes projectile motion with an initial horizontal velocity $v$ and zero initial vertical velocity.The time taken to fall a height $h$ is given by $h = \frac{1}{2}gt^2$,so $t = \sqrt{\frac{2h}{g}}$.The horizontal distance $d$ traveled is $d = v \times t$.$d = \sqrt{\mu Rg} \times \sqrt{\frac{2h}{g}} = \sqrt{2\mu Rh}$.

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

Difficult

$A$ small mass $m$ rests at the edge of a horizontal disc of radius $R$. The coefficient of static friction between the mass and the disc is $\mu$. The disc is rotated about its axis at an angular velocity such that the mass slides off the disc and lands on the floor $h$ meters below. What was its horizontal distance of travel from the point it left the disc?

A
$\sqrt{\mu h}$
B
$\sqrt{\mu (R + h)^2}$
C
$\sqrt{\mu Rh}$
D
$\sqrt{2\mu Rh}$

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Class 11 Questions

Class 11

Physics Questions

Chapter

Newton's Laws of Motion and Friction

Subtopic

Circular motion with Friction

On a dry road,the maximum speed of a vehicle along a circular path is $V$. When the road becomes wet,the maximum speed becomes $\frac{V}{2}$. If the coefficient of friction of the dry road is $\mu$,then the coefficient of friction of the wet road is:

MediumMHT CET 2023

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$A$ gramophone record is revolving with an angular velocity $\omega$. $A$ coin is placed at a distance $r$ from the centre of the record. The static coefficient of friction is $\mu$. The coin will revolve with the record if

MediumAIPMT 2010

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$A$ small object placed on a rotating horizontal turntable just slips when it is placed at a distance $4\, cm$ from the axis of rotation. If the angular velocity of the turntable is doubled,the object slips when its distance from the axis of rotation is (in $, cm$)

Medium

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The maximum speed of a car on a road turn of radius $30\,m$; if the coefficient of friction between the tyres and the road is $0.4$; will be ........ $m/s$. (in $.84$)

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$A$ person is driving a vehicle at a uniform speed of $5 \text{ ms}^{-1}$ on a level curved track of radius $5 \text{ m}$. The coefficient of static friction between the tyres and the road is $0.1$. Will the person slip while taking the turn with the same speed? (Take $g = 10 \text{ ms}^{-2}$)

EasyKCET 2014

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On a dry road,the maximum speed of a vehicle along a circular path is $V$. When the road becomes wet,the maximum speed becomes $\frac{V}{2}$. If the coefficient of friction of the dry road is $\mu$,then the coefficient of friction of the wet road is:

$A$ gramophone record is revolving with an angular velocity $\omega$. $A$ coin is placed at a distance $r$ from the centre of the record. The static coefficient of friction is $\mu$. The coin will revolve with the record if

$A$ small object placed on a rotating horizontal turntable just slips when it is placed at a distance $4\, cm$ from the axis of rotation. If the angular velocity of the turntable is doubled,the object slips when its distance from the axis of rotation is (in $, cm$)

The maximum speed of a car on a road turn of radius $30\,m$; if the coefficient of friction between the tyres and the road is $0.4$; will be ........ $m/s$. (in $.84$)

$A$ person is driving a vehicle at a uniform speed of $5 \text{ ms}^{-1}$ on a level curved track of radius $5 \text{ m}$. The coefficient of static friction between the tyres and the road is $0.1$. Will the person slip while taking the turn with the same speed? (Take $g = 10 \text{ ms}^{-2}$)

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