A block of mass $50 \,kg$ can slide on a rough horizontal surface. The coefficient of friction between the block and the surface is $0.6$. The least force of pull acting at an angle of $30^°$ to the upward drawn vertical which causes the block to just slide is ........ $N$
$29.43$
$219.6$
$21.96$
$294.3$
A block of mass $4\,kg$ is placed on a rough horizontal plane A time dependent force $F = kt^2$ acts on the block, where $k = 2\,N/s^2$. Coefficient of friction $\mu = 0.8$. Force of friction between block and the plane at $t = 2\,s$ is ....... $N$
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
A circular racetrack of radius $300\; m$ is banked at an angle of $15^o$. If the coefficient of friction between the wheels of a race-car and the road is $0.2$, what is the
$(a)$ optimum speed of the racecar to avoid wear and tear on its tyres, and
$(b)$ maximum permissible speed to avoid slipping ?
A block of mass $m$ is stationary on a rough plane of mass $M$ inclined at an angle $\theta$ to the horizontal, while the whole set up is accelerating upwards at an acceleration $\alpha$. If the coefficient of friction between the block and the plane is $\mu$, then the force that the plane exerts on the block is
A heavy body of mass $25\, kg$ is to be dragged along a horizontal plane $\left( {\mu = \frac{1}{{\sqrt 3 }}} \right).$ The least force required is ........ $kgf$