(D) The maximum speed $V_{\max}$ on a banked road with friction is given by $V_{\max} = \sqrt{\frac{rg(\mu + \tan \theta)}{1 - \mu \tan \theta}}$.The

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(D) The maximum speed $V_{\max}$ on a banked road with friction is given by $V_{\max} = \sqrt{\frac{rg(\mu + \tan \theta)}{1 - \mu \tan \theta}}$.The optimum speed $V_o$ (where no friction is required) is given by $V_o = \sqrt{rg \tan \theta}$.Given $\theta = 45^{\circ}$ and $V_{\max} = 2V_o$.Substituting the expressions: $\sqrt{\frac{rg(\mu + \tan \theta)}{1 - \mu \tan \theta}} = 2 \sqrt{rg \tan \theta}$.Squaring both sides: $\frac{\mu + \tan \theta}{1 - \mu \tan \theta} = 4 \tan \theta$.Since $\tan 45^{\circ} = 1$, we have $\frac{\mu + 1}{1 - \mu} = 4(1)$.$\mu + 1 = 4 - 4\mu$.$5\mu = 3$.$\mu = \frac{3}{5} = 0.6$.

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

Medium

$A$ car is moving on a circular track banked at an angle of $45^{\circ}$. If the maximum permissible speed of the car to avoid slipping is twice the optimum speed of the car to avoid the wear and tear of the tyres, then the coefficient of static friction between the wheels of the car and the road is

TS EAMCET 2024 All TS EAMCET

A
$0.3$
B
$0.5$
C
$0.4$
D
$0.6$

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Class 11

Physics Questions

Chapter

Newton's Laws of Motion and Friction

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Circular motion with Friction

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$A$ block of mass $m$ is kept on a horizontal turntable at a distance $x$ from the center. If the coefficient of friction between the block and the surface of the turntable is $\mu$,what is the maximum angular speed of the table so that the block does not slip?

Medium

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$A$ motor car has a width of $1.1 \ m$ between its wheels. Its center of gravity is $0.62 \ m$ above the ground and the coefficient of friction between the wheels and the road is $0.8$. What is the maximum possible speed in $m/s$ if the center of gravity moves in a circle of radius $15 \ m$ on a horizontal road surface?

Medium

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$A$ disc revolves with a speed of $33 \frac{1}{3} \; rev/min$,and has a radius of $15 \; cm$. Two coins are placed at $4 \; cm$ and $14 \; cm$ away from the centre of the record. If the coefficient of friction between the coins and the record is $0.15$,which of the coins will revolve with the record?

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$A$ motorcyclist moving with a velocity of $72\, km/h$ on a flat road takes a turn at a point where the radius of curvature of the road is $20\, m$. The acceleration due to gravity is $10\, m/s^2$. In order to avoid skidding,he must not bend with respect to the vertical plane by an angle greater than

Medium

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$A$ block of mass $m$ is kept on a horizontal turntable at a distance $x$ from the center. If the coefficient of friction between the block and the surface of the turntable is $\mu$,what is the maximum angular speed of the table so that the block does not slip?

$A$ coin placed on a rotating table just slips if it is placed at a distance $4r$ from the centre. On doubling the angular velocity of the table,the coin will just slip when at a distance from the centre equal to

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