A solid cylinder of mass $M$ and radius $R$ rolls without slipping down a rough inclined plane of angle $heta$. A block of the same mass $M$ slides down a frictionless inclined plane of the same angle $heta$. If both start from rest at the same height, what is the ratio of the linear speeds of the cylinder and the block when they reach the bottom?

On the horizontal surface of a truck $\left( {\mu = 0.6} \right)$, a block of mass 1 kg is placed. If the truck is accelerating at the rate of $5m/se{c^2}$ then frictional force on the block will be

A body of mass 2 kg is being dragged with uniform velocity of 2 m/s on a rough horizontal plane. The coefficient of friction between the body and the surface is 0.20. The amount of heat generated in 5 sec is (J=4.2 joule/cal and $\;g = 9.8\;m/{s^2})$

If a block slides down a frictionless inclined plane with an angle of inclination $heta$, what is its acceleration?

Consider a car moving along a straight horizontal road with a speed of 72 km/h. If the coefficient kinetic friction between the tyres and the road is 0.5, the shortest distance in which the car can be stopped is $\left[ {g = 10\;m{s^{ - 2}}} \right]$

A force of 98 N is required to just start moving a body of mass 100 kg over ice. The coefficient of static friction is

Two blocks of masses $m_1$ and $m_2$ are connected by a light string passing over a frictionless pulley at the top of a smooth inclined plane of angle $heta$. If $m_1 > m_2\sinheta$, what is the acceleration of the system?

A block slides down a frictionless inclined plane of inclination $heta$. If $g$ is the acceleration due to gravity, its acceleration down the plane is:

A rectangular block has a square base measuring a×a, and its height is $h$. Its moves on a horizontal surface in a direction perpendicular to one of its edges. The coefficient of friction is $\mu$. It will topple if

A marble block of mass 2 kg lying on ice when given a velocity of $6\;{\rm{m}}{{\rm{s}}^{ - 1}}$ is stopped by friction in 10 s. Then the coefficient of friction is

A bend in a level road has a radius of 80 m. Find the maximum speed which a car turning the bend may have without skidding, if $\mu = 0.25$