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A cyclist riding the bicycle at a speed of $14 \sqrt{3} \,m / s$ takes a turn around a circular road of radius $20 \sqrt{3} \,m$ without skidding. What is his inclination to the vertical?
A circular road of radius $1000 \,m$ has banking angle ${45^o}$. The maximum safe speed of a car having mass $2000 \,kg$ will be, if the coefficient of friction between tyre and road is $0.5$ ....... $m/s$
A ball of mass $0.25\, kg$ attached to the end of a string of length $1.96 \,m$ is moving in a horizontal circle. The string will break if the tension is more than $25 \,N$. .......... $m/s$ is the maximum speed with which the ball can be moved
A block starts moving up an inclined plane of inclination $30^{\circ}$ with an initial velocity of $v_{0}$. It comes back to its initial position with velocity $\frac{v_{0}}{2} .$ The value of the coefficient of kinetic friction between the block and the inclined plane is close to $\frac{ I }{1000},$ The nearest integer to $I$ is......
A motorcycle is going on an overbridge of radius $R$. The driver maintains a constant speed. As the motorcycle is ascending on the overbridge, the normal force on it
A block of mass $m$ lying on a rough horizontal plane is acted upon by a horizontal force $P$ and another force $Q$ inclined at an angle $\theta $ to the vertical. The block will remain in equilibrium, if the coefficient of friction between it and the surface is
A uniform rod of length $l$ is being rotated in a horizontal plane with a constant angular speed about an axis passing through one of its ends. If the tension generated in the rod due to rotation is $T(x)$ at a distance $x$ from the axis, then which of the following graphs depicts it most closely?
As shown in the figure, two strings of length $l$ each are attached with a vertical axis $AB$ of length $l$. Strings are $AC$ and $BC$. At point $C$ a point mass m is attached. Mass rotates about axis with angular velocity. Tensions in $AB$ and $BC$ are $T_1$ and $T_2$ respectively. Choose the $CORRECT$ alternative :-
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
Radius of the curved road on national highway is $R$. Width of the road is $b$. The outer edge of the road is raised by $h$ with respect to inner edge so that a car with velocity $v$ can pass safe over it. The value of $h$ is