A body of mass $10$ kg slides along a rough horizontal surface. The coefficient of friction is $1/\sqrt 3 $. Taking $g = 10\,m/{s^2}$, the least force which acts at an angle of $30^o $ to the horizontal is ...... $N$

  • A

    $25$

  • B

    $100$

  • C

    $50$

  • D

    $\frac{{50}}{{\sqrt 3 }}$

Similar Questions

A block of mass $5\, kg$ is $(i)$ pushed in case $(A)$ and $(ii)$ pulled in case $(B)$, by a force $F = 20\, N$, making an angle of $30^o$ with the horizontal, as shown in the figures. The coefficient of friction between the block and floor is $\mu = 0.2$. The difference between the accelerations of the block, in case $(B)$ and case $(A)$ will be ........ $ms^{-2}$ .$(g = 10\, ms^{-2})$

  • [JEE MAIN 2019]

A rectangular box lies on a rough inclined surface. The coefficient of friction between the surface and the box is $\mu $. Let the mass of the box be $m$.

$(a)$ At what angle of inclination $\theta $ of the plane to the horizontal will the box just start to slide down the plane ?

$(b)$ What is the force acting on the box down the plane, if the angle of inclination of the plane is increased to $\alpha > \theta $ ?

$(c)$ What is the force needed to be applied upwards along the plane to make the box either remain stationary or just move up with uniform speed ?

$d)$ What is the force needed to be applied upwards along the plane to make the box move up the plane with acceleration $a$ ?

A block of mass $m$ rests on a rough inclined plane. The coefficient of friction between  the surface and the block is $\mu$. At what angle of inclination $\theta$ of the plane to  the horizontal will the block just start to slide down the plane?

An inclined plane is bent in such a way that the vertical cross-section is given by $y =\frac{ x ^{2}}{4}$ where $y$ is in vertical and $x$ in horizontal direction. If the upper surface of this curved plane is rough with coefficient of friction $\mu=0.5,$ the maximum height in $cm$ at which a stationary block will not slip downward is............$cm$

  • [JEE MAIN 2021]

Aball of mass $m$ is thrown vertically upwards.Assume the force of air resistance has magnitude proportional to the velocity, and direction opposite to the velocity's. At the highest point, the ball's acceleration is