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The coefficient of friction between a body and the surface of an inclined plane at $45^°$ is $0.5.$ If $g = 9.8\,m/{s^2}$, the acceleration of the body downwards in $m/{s^2}$ is
A cyclist moves in a circular track of radius $100$ m. If the coefficient of friction is $0.2$, then the maximum velocity with which the cyclist can take the turn with leaning inwards is ...... $m/s$
A curved in a level road has a radius $75\, m$. The maximum speed of a car turning this curved road can be $30 \,m / s$ without skidding. If radius of curved road is changed to $48\, m$ and the coefficient of friction between the tyres and the road remains same, then maximum allowed speed would be .........$m / s$.
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 $g = 9.8\,m/{s^2})$
In the shown arrangement mass of $A = 1\,\,kg$ mass of $B = 2\,\,kg.$ Coefficient of friction between $A $ and $B = 0.2.$ There is no friction between $B$ and ground. The frictional force exerted by $A$ on $B$ equals to
An object of mass $1 \,kg$ moving on a horizontal surface with initial velocity $8 \,m / s$ comes to rest after $10 \,s$. If one wants to keep the object moving on the same surface with velocity $8 \,m / s$ the force required is ...... $N$
A uniform rod of length $L$ and mass $M$ has been placed on a rough horizontal surface. The horizontal force $F$ applied on the rod is such that the rod is just in the state of rest. If the coefficient of friction varies according to the relation $\mu = Kx$ where $K$ is a $+$ ve constant. Then the tension at mid point of rod is
A block of mass $m$ (initially at rest) is sliding up (in vertical direction) against a rough vertical wall with the help of a force $F$ whose magnitude is constant but direction is changing. $\theta = {\theta _0}t$ where $t$ is time in sec. At $t$ = $0$ , the force is in vertical upward direction and then as time passes its direction is getting along normal, i.e., $\theta = \frac{\pi }{2}$ .The value of $F$ so that the block comes to rest when $\theta = \frac{\pi }{2}$ , is