A child weighing $25$ kg slides down a rope hanging from the branch of a tall tree. If the force of friction acting against him is $2\, N$, ........ $m/s^2$ is the acceleration of the child (Take $g = 9.8\,m/{s^2})$
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A block weighs $W$ is held against a vertical wall by applying a horizontal force $F$. The minimum value of $F$ needed to hold the block is $[\mu < 1]$
A solid hemisphere of weight $P$ rests with its curved surface in contact with a rough inclined plane. A weight $Q$ is placed at some point on the rim of the hemisphere to keep its plane surface horizontal then its minimum coefficient of friction is
The force required just to move a body up an inclined plane is double the force required just to prevent the body sliding down. If the coefficient of friction is $0.25$, the angle of inclination of the plane is ...... $^o$
At time $t=0$, a disk of radius $1 m$ starts to roll without slipping on a horizontal plane with an angular acceleration of $\alpha=\frac{2}{3} rad s ^{-2}$. A small stone is stuck to the disk. At $t=0$, it is at the contact point of the disk and the plane. Later, at time $t=\sqrt{\pi} s$, the stone detaches itself and flies off tangentially from the disk. The maximum height (in $m$ ) reached by the stone measured from the plane is $\frac{1}{2}+\frac{x}{10}$. The value of $x$ is. . . . . . .[Take $g=10 m s ^{-2}$.]
A $20\, kg$ block is initially at rest on a rough horizontal surface. A horizontal force of $75 \,N$ is required to set the block in motion. After it is in motion, a horizontal force of $60\, N$ is required to keep the block moving with constant speed. The coefficient of static friction is
In figure, two blocks $M$ and $m$ are tied together with an inextensible and light string. The mass $M$ is placed on a rough horizontal surface with coefficient of friction $\mu$ and the mass $m$ is hanging vertically against a smooth vertical wall. The pulley is frictionless. When the downward acceleration of the elevator becomes equal to $g$, then
A vehicle is moving with a velocity $v$ on a curved road of width $b$ and radius of curvature $R.$ For counteracting the centrifugal force on the vehicle, the difference in elevation required in between the outer and inner edges of the road is
A block slides down an inclined plane of slope of angle $\theta $ with a constant velocity. It is then projected up the plane with an initial velocity $u$. The distance upto which it will rise before coming to rest is