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A body of mass $\mathrm{m}$ is kept on a rough horizontal surface (coefficient of friction $=\mu$ ) A horizontal force is applied on the body, but it does not move. The resultant of normal reaction and the frictional force acting on the object is given by $\mathrm{F},$ where $\mathrm{F}$ is
A rectangular block has a square base measuring $a \times a$ and its height is $h$. It moves on a horizontal surface in a direction perpendicular to one of the edges. The coefficient of friction is $\mu$. It will topple if
Calculate the maximum acceleration (in $m s ^{-2}$) of a moving car so that a body lying on the floor of the car remains stationary. The coefficient of static friction between the body and the floor is $0.15$ $\left( g =10 m s ^{-2}\right)$.
A block of mass $m$ is on an inclined plane of angle $\theta$. The coefficient of friction between the block and the plane is $\mu$ and $\tan \theta>\mu$. The block is held stationary by applying a force $\mathrm{P}$ parallel to the plane. The direction of force pointing up the plane is taken to be positive. As $\mathrm{P}$ is varied from $\mathrm{P}_1=$ $m g(\sin \theta-\mu \cos \theta)$ to $P_2=m g(\sin \theta+\mu \cos \theta)$, the frictional force $f$ versus $P$ graph will look like
A block of weight $W$ rests on a horizontal floor with coefficient of static friction $\mu .$ It is desired to make the block move by applying minimum amount of force. The angle $\theta $ from the horizontal at which the force should be applied and magnitude of the force $F$ are respectively.
As shown in the figure, a block of mass $\sqrt{3}\, kg$ is kept on a horizontal rough surface of coefficient of friction $\frac{1}{3 \sqrt{3}}$. The critical force to be applied on the vertical surface as shown at an angle $60^{\circ}$ with horizontal such that it does not move, will be $3 x$. The value of $3x$ will be
$\left[ g =10 m / s ^{2} ; \sin 60^{\circ}=\frac{\sqrt{3}}{2} ; \cos 60^{\circ}=\frac{1}{2}\right]$
A stone weighing $1$ kg and sliding on ice with a velocity of $2$ m/s is stopped by friction in $10$ sec. The force of friction (assuming it to be constant) will be ......... $N$
The maximum speed of a car on a road-turn of radius $30\, m$, if the coefficient of friction between the tyres and the road is $0.4$, will be .......... $m/sec$