A car is moving on a horizontal circular road of radius $0.1 \,km$ with constant speed. If coefficient of friction between tyres of car and road is $0.4$, then speed of car may be ......... $m / s$ $\left(g=10 \,m / s ^2\right)$
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A car of mass $1000\, kg$ negotiates a banked curve of radius $90\, m$ on a frictionless road. If the banking angle is $45^o $, the speed of the car is ....... $ms^{-1}$
A block of mass $m$ is placed on a surface having vertical cross section given by $y=x^2 / 4$. If coefficient of friction is $0.5$ , the maximum height above the ground at which block can be placed without slipping is:
A ball of mass $0.1\, Kg$. is whirled in a horizontal circle of radius $1\, m$. by means of a string at an initial speed of $10\, R.P.M.$ Keeping the radius constant, the tension in the string is reduced to one quarter of its initial value. The new speed is ....... $r.p.m.$
A block of mass $10\; \mathrm{kg}$ is in contact against the inner wall of a hollow cylindow cylindrical drum of radius $1 \;\mathrm{m}$. The coeffident of friction between the block and the inner wall of the cylinder is $0.1$. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis, will be: ......$rad/s$ $\left(g-10 m / s^{2}\right)$
Someone is using a scissors to cut a wire of circular cross section and negligible weight. The wire slides in the direction away from the hinge until the angle between the scissors blades becomes $2 \alpha$. The friction coefficient between the blades and the wire, is :-
Blocks shown in figure moves with constant velocity $10 \,m / s$ towards right. All surfaces in contact are rough. The friction force applied by $B$ on $A$ is ...........$N$