An inclined plane is bent in such a way that the vertical cross-section is given by $y =\frac{ x ^{2}}{4}$ where $y$ is in vertical and $x$ in horizontal direction. If the upper surface of this curved plane is rough with coefficient of friction $\mu=0.5,$ the maximum height in $cm$ at which a stationary block will not slip downward is............$cm$

Which is a suitable method to decrease friction

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 Identify the correct statement $(s)$ related to the tension $T$ in the string

A block of mass $70\,kg$ is kept on a rough horizontal surface $(\mu = 0.4)$. A person is trying to pull the block by applying a horizontal force, but the block is not moving. The net contact force exerted by the surface on the block is $F$, then

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 block of mass $50 \,kg$ can slide on a rough horizontal surface. The coefficient of friction between the block and the surface is $0.6$. The least force of pull acting at an angle of $30^°$ to the upward drawn vertical which causes the block to just slide is ........ $N$