A particle is moving along the circle $x^2 + y^2 = a^2$ in anti clock wise direction. The $x-y$ plane is a rough horizontal stationary surface. At the point $(a\, cos\theta , a\, sin\theta )$, the unit vector in the direction of friction on the particle is:
$\cos \theta \,\hat i + \sin \theta \,\hat j$
$ - \left( {\cos \theta \,\hat i + \sin \theta \,\hat j} \right)$
$\sin \theta \,\hat i - \cos \theta \,\hat j$
$\cos \theta \,\hat i - \sin \theta \,\hat j$
A block $A$ of mass $m_1$ rests on a horizontal table. A light string connected to it passes over a frictionless pully at the edge of table and from its other end another block $B$ of mass $m_2$ is suspended. The coefficient of kinetic friction between the block and the table is $\mu _k.$ When the block $A$ is sliding on the table, the tension in the string is
Consider a block and trolley system as shown in figure. If the coefficient of kinetic friction between the trolley and the surface is $0.04$ , the acceleration of the system in $\mathrm{ms}^{-2}$ is :
(Consider that the string is massless and unstretchable and the pulley is also massless and frictionless):
Two blocks $A$ and $B$ of masses $5 \,kg$ and $3 \,kg$ respectively rest on a smooth horizontal surface with $B$ over $A$. The coefficient of friction between $A$ and $B$ is $0.5$. The maximum horizontal force (in $kg$ wt.) that can be applied to $A$, so that there will be motion of $A$ and $B$ without relative slipping, is
A body of mass $2$ kg is moving on the ground comes to rest after some time. The coefficient of kinetic friction between the body and the ground is $0.2$. The retardation in the body is ...... $m/s^2$
A body of mass $10\,kg$ is moving with an initial speed of $20\,m / s$. The body stops after $5\,s$ due to friction between body and the floor. The value of the coefficient of friction is (Take acceleration due to gravity $g =10\; ms ^{-2}$)