A body of mass $\mathrm{m}$ is kept on a rough horizontal surface (coefficient of friction $=\mu$ ) A horizontal force is applied on the body, but it does not move. The resultant of normal reaction and the frictional force acting on the object is given by $\mathrm{F},$ where $\mathrm{F}$ is
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A block of mass $m$ is moving with a constant acceleration a on a rough plane. If the coefficient of friction between the block and ground is $\mu $, the power delivered by the external agent after a time $t$ from the beginning is equal to
A girl holds a book of mass $m$ against a vertical wall with a horizontal force $F$ using her finger, so that the book does not move. The frictional force on the book by the wall is
A small object placed on a rotating horizontal turn table just slips when it is placed at a distance $4\, cm$ from the axis of rotation. If the angular velocity of the turn-table is doubled, the object slips when its distance from the axis of rotation is
A road is $10\, m$ wide. Its radius of curvature is $50\, m$. The outer edge is above the lower edge by a distance of $1.5\, m$. This road is most suited for the velocity .......... $m/\sec$
A hollow vertical cylinder of radius $R$ is rotated with angular velocity $\omega$ about an axis through its center. What is the minimum coefficient of static friction necessary to keep the mass $M$ suspended on the inside of the cylinder as it rotates?
A bullet of mass $20\, g$ travelling horizontally with a speed of $500 \,m/s$ passes through a wooden block of mass $10.0 \,kg$ initially at rest on a surface. The bullet emerges with a speed of $100\, m/s$ and the block slides $20 \,cm$ on the surface before coming to rest, the coefficient of friction between the block and the surface. $(g = 10\, m/s^2)$
A particle moves in a circular orbit under the action of a central attractive force inversely proportional to the distance $'r'$. The speed of the particle is
A rope of length $L$ and mass $M$ is being pulled on a rough horizontal floor by a constant horizontal force $F$ = $Mg$ . The force is acting at one end of the rope in the same direction as the length of the rope. The coefficient of kinetic friction between rope and floor is $1/2$ . Then, the tension at the midpoint of the rope is