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 of mass $10 \,kg$ is held at rest against a rough vertical wall $[\mu=0.5]$ under the action a force $F$ as shown in figure. The minimum value of $F$ required for it is ............ $N$ $\left(g=10 \,m / s ^2\right)$
Imagine the situation in which the given arrangement is placed inside a trolley that can move only in the horizontal direction, as shown in figure. If the trolley is accelerated horizontally along the positive $x$ -axis with $a_0$, then Choose the correct statement $(s)$.
A block of mass $10 kg$ is moving on a rough surface as shown in figure. The frictional force acting on block is ...... $N$
Two bodies $A$ and $B$ of masses $5 kg$ and $10 kg$ in contact with each other rest on a table against a rigid wall. The coefficient of friction between the bodies and the table is $0.15$. A force of 200 $N$ is applied hortzontally to $A$. What are $(a)$ the reaction of the partition $(b)$ the action-reaction forces between $A$ and $B ?$ What happens when the wall is removed? Does the answer to $(b)$ change, when the bodies are in motion? Ignore the difference between $\mu_{ s }$ and $\mu_{ k }$
A block of mass $m$ is placed on a surface with a vertical cross section given by $y = \frac{{{x^3}}}{6}$ If the coefficient of friction is $0.5$,the maximum height above the ground at which the block can be placed without slipping is: