Two masses $m_1 = 5\ kg$ and $m_2 = 10\ kg$, connected by an inextensible string over a frictionless pulley, are moving as shown in the figure. The coefficient of friction of horizontal surface is $0.15$. The minimum weight $m$ that should be put on top of $m_2$ to stop the motion is ........ $kg$
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A hemispherical bowl of radius $R$ is rotated about its axis of symmetry which is kept vertical with angular velocity $\omega $ . A small block is kept in the bowl. It remains stationary relative to the bowl surface at a position where the radius makes an angle $\theta $ with the vertical. The friction is absent. The value of $\theta $ is
If a ladder weighing $250\,N$ is placed against a smooth vertical wall having coefficient of friction between it and floor is $0.3$, then what is the maximum force of friction available at the point of contact between the ladder and the floor ........ $N$
Two masses $M$ and $m$ are attached to a vertical axis by weightless threads of combined length $l$. They are set in rotational motion in a horizontal plane about this axis with constant angular velocity $\omega $. If the tensions in the threads are the same during motion, the distance of $M$ from the axis is
A block of mass $m$ is placed on a surface with a vertical coss 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
Two blocks $( m =0.5\, kg$ and $M =4.5\, kg$ ) are arranged on a horizontal frictionless table as shown in figure. The coefficient of static friction between the two blocks is $\frac{3}{7} .$ Then the maximum horizontal force that can be applied on the larger block so that the blocks move together is ......... $N.$ (Round off to the Nearest Integer) [Take g as $9.8\, ms ^{-2}$ ]
A uniform rod of length $L$ and mass $M$ has been placed on a rough horizontal surface. The horizontal force $F$ applied on the rod is such that the rod is just in the state of rest. If the coefficient of friction varies according to the relation $\mu = Kx$ where $K$ is a $+$ ve constant. Then the tension at mid point of rod is
The coefficient of static friction between a wooden block of mass $0.5\, kg$ and a vertical rough wall is $0.2$ The magnitude of horizontal force that should be applied on the block to keep it adhere to the wall will be $N$ $\left[ g =10\, ms ^{-2}\right]$
A bullet of mass $0.1\,kg$ moving horizontally with speed $400\,ms ^{-1}$ hits a wooden block of mass $3.9\,kg$ kept on a horizontal rough surface. The bullet gets embedded into the block and moves $20\,m$ before coming to rest. The coefficient of friction between the block and the surface is $........$ $\left(\text { Given } g=10 \,ms ^2\right. \text { ) }$