A vehicle is moving with speed $v$ on a curved road of radius $r$. The coefficient of friction between the vehicle and the road is $\mu$. The angle $\theta$ of banking needed is given by
$\tan \theta=\frac{v^2-\mu r g}{v^2-r g}$
$\tan \theta=\frac{v^2-\mu r g}{v^2+\mu r g}$
$\tan \theta=\frac{v^2-\mu r g}{r g+\mu v^2}$
$\tan \theta=\frac{\mu r \cdot g-v^2}{r g+\mu v^2}$
A force of $19.6\, N$ when applied parallel to the surface just moves a body of mass $10 \,kg$ kept on a horizontal surface. If a $5\, kg$ mass is kept on the first mass, the force applied parallel to the surface to just move the combined body is........ $N.$
A heavy uniform chain lies on a horizontal table-top. If the coefficient of friction between the chain and table surface is $0.25$, then the maximum fraction of length of the chain, that can hang over one edge of the table is ...... $\%$
A block is moving on an inclined plane making an angle $45^{\circ}$ with the horizontal and the coefficient of friction is $\mu$. The force required to just push it up the inclined plane is $3$ times the force required to just prevent it from sliding down. If we define $N=10 \ \mu$, then $N$ is
A block of mass $5\, kg$ is kept on a rough horizontal floor. It is given a velocity $33\, m/s$ towards right. A force of $20\sqrt {2\,} \,N$ continuously acts on the block as shown in the figure. If the coefficient of friction between block and floor is $0.5$ the velocity of block after $3\, seconds$ is ........ $m/s$ ($g = 10\, m/s^2$)
Which of the following statements is not true