(A) The work done by friction is given by $W_f = -\int \mu N \, ds$. For route $1$,the surface is convex,so the normal force $N_1 = mg \cos \theta - \

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(A) The work done by friction is given by $W_f = -\int \mu N \, ds$. For route $1$,the surface is convex,so the normal force $N_1 = mg \cos \theta - \frac{mv^2}{r}$. For route $2$,the surface is concave,so the normal force $N_2 = mg \cos \theta + \frac{mv^2}{r}$. Since $N_2 > N_1$,the frictional force $f = \mu N$ is greater on route $2$ than on route $1$. As the work done against friction is greater on route $2$,more mechanical energy is dissipated as heat on route $2$. Therefore,the final kinetic energy and speed at point $B$ will be greater for route $1$.

Class 11 Physics Newton's Laws of Motion and Friction Kinetic Friction and Motion on Rough Horizontal Surface

Medium

$A$ small body slips,subject to the force of friction,from point $A$ to point $B$ along two curved surfaces of equal radius,first along route $1$,then along route $2$. Friction does not depend on the speed and the coefficient of friction on both routes is the same. In which case will the body's speed at $B$ be greater?

A
speed is greater in case $1$
B
speed is greater in case $2$
C
speed is same in both cases
D
cannot be determined

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Class 11 Questions

Class 11

Physics Questions

Chapter

Newton's Laws of Motion and Friction

Subtopic

Kinetic Friction and Motion on Rough Horizontal Surface

$A$ block of mass $0.5 \ kg$ is at rest on a horizontal table. The coefficient of kinetic friction between the table and the block is $0.2$. If a horizontal force of $5 \ N$ is applied on the block,the kinetic energy of the block in a time of $4 \ s$ is (Acceleration due to gravity $= 10 \ m/s^2$). (in $J$)

MediumTS EAMCET 2024

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$A$ block of mass $5\, kg$ is on a rough horizontal surface and is at rest. Now a force of $24\, N$ is imparted to it with negligible impulse. If the coefficient of kinetic friction is $0.4$ and $g = 9.8\, m/s^2$,then the acceleration of the block is ........ $m/s^2$.

Medium

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$A$ $2 \, kg$ block on ice is given a velocity of $6 \, m/s$. If it comes to rest in $10 \, s$,what is the coefficient of friction?

Easy

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$A$ block of mass $5\,kg$ is placed at rest on a table with a rough surface. If a force of $30\,N$ is applied parallel to the surface of the table,the block slides through a distance of $50\,m$ in $10\,s$. Calculate the coefficient of kinetic friction. (Given: $g = 10\,m/s^2$)

MediumJEE MAIN 2023

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$A$ man of mass $60 \, kg$ slides down a pole by applying a force of $600 \, N$ on it. If the coefficient of friction between the hands and the pole is $0.5$,then the acceleration of the man is ............ $m/s^2$ $(g = 10 \, m/s^2)$.

Difficult

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$A$ block of mass $5\, kg$ is on a rough horizontal surface and is at rest. Now a force of $24\, N$ is imparted to it with negligible impulse. If the coefficient of kinetic friction is $0.4$ and $g = 9.8\, m/s^2$,then the acceleration of the block is ........ $m/s^2$.

$A$ $2 \, kg$ block on ice is given a velocity of $6 \, m/s$. If it comes to rest in $10 \, s$,what is the coefficient of friction?

$A$ block of mass $5\,kg$ is placed at rest on a table with a rough surface. If a force of $30\,N$ is applied parallel to the surface of the table,the block slides through a distance of $50\,m$ in $10\,s$. Calculate the coefficient of kinetic friction. (Given: $g = 10\,m/s^2$)

$A$ man of mass $60 \, kg$ slides down a pole by applying a force of $600 \, N$ on it. If the coefficient of friction between the hands and the pole is $0.5$,then the acceleration of the man is ............ $m/s^2$ $(g = 10 \, m/s^2)$.

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