In figure, two blocks $M$ and $m$ are tied together with an inextensible and light string. The mass $M$ is placed on a rough horizontal surface with coefficient of friction $\mu$ and the mass $m$ is hanging vertically against a smooth vertical wall. The pulley is frictionless. Choose the correct statement $(s)$ related to the tension $T$ in the string
Difficult
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A disc with a flat small bottom beaker placed on it at a distance $R$ from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity $\omega$. The coefficient of static friction between the bottom of the beaker and the surface of the disc is $\mu$. The beaker will revolve with the disc if
A block of mass $5\, kg$ is on a rough horizontal surface and is at rest. Now a force of $24\, N $is imparted to it with negligible impulse. If the coefficient of kinetic friction is $0.4$ and $g = 9.8\,m/{s^2}$, then the acceleration of the block is ........ $m/s^2$
A $20\, kg$ block is initially at rest on a rough horizontal surface. A horizontal force of $75 \,N$ is required to set the block in motion. After it is in motion, a horizontal force of $60\, N$ is required to keep the block moving with constant speed. The coefficient of static friction is
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
The coefficient of friction between a body and the surface of an inclined plane at $45^°$ is $0.5.$ If $g = 9.8\,m/{s^2}$, the acceleration of the body downwards in $m/{s^2}$ is
A bullet of mass $20\, g$ travelling horizontally with a speed of $500 \,m/s$ passes through a wooden block of mass $10.0 \,kg$ initially at rest on a surface. The bullet emerges with a speed of $100\, m/s$ and the block slides $20 \,cm$ on the surface before coming to rest, the coefficient of friction between the block and the surface. $(g = 10\, m/s^2)$
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: