A body is sliding down an inclined plane (angle of inclination $45^o$). If the coefficient of friction is $0.5$ and $g = 9.8\, m/s^2$. then the acceleration of the body downwards in $m/s^2$ is
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In the diagram, $BAC$ is a rigid fixed rough wire and angle $BAC$ is $60^o$. $P$ and $Q$ are two identical rings of mass $m$ connected by a light elastic string of natural length $2a$ and elastic constant $\frac{mg}{a}$. If $P$ and $Q$ are in equilibrium when $PA = AQ = 3a$ then the least coefficient of friction between the ring and the wire is $\mu$. Then value of $\mu + \sqrt 3 $ is :-
A block of mass $m$ lying on a rough horizontal plane is acted upon by a horizontal force $P$ and another force $Q$ inclined an at an angle $\theta $ to the vertical. The minimum value of coefficient of friction between the block and the surface for which the block will remain in equilibrium is
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 body of mass $'m '$ is tied to one end of a spring and whirled round in a horizontal plane with a constant angular velocity. The elongation in the spring is $1\, cm$. If the angular velocity is doubled, the elongation in the spring is $5\, cm$. The original length of the spring is ......... $cm$
If the radius of curvature of the path of two particles of same mass are in the ratio $3:4,$ then in order to have constant centripetal force, their velocities will be in the ratio of:
A block of mass $M$ is being pulled along rough horizontal surface. The coefficient of friction between the block and the surface is $\mu $. If another block of mass $M/2$ is placed on the block and it is again pulled on the surface, the coefficient of friction between the block and the surface will be
A block of mass $10 \,kg$ is held at rest against a rough vertical wall $[\mu=0.5]$ under the action a force $F$ as shown in figure. The minimum value of $F$ required for it is ............ $N$ $\left(g=10 \,m / s ^2\right)$