$A$ body is sliding down an inclined plane (angle of inclination $45^{\circ}$). If the coefficient of friction is $0.5$ and $g = 9.8\, m/s^2$,then the acceleration of the body downwards in $m/s^2$ is

Consider three masses $m_1, m_2$ and $m_3$ $(m_1 > m_2 > m_3)$ that are at rest on an inclined plane as shown in the figure. The angle of inclination $(\theta)$ of the plane is gradually increased until the masses just begin to slide. (Assume the coefficient of static friction between the masses and the surface is constant). Then,which of the following statements is correct?

Two blocks $A$ and $B$ of equal masses are sliding down along straight parallel lines on an inclined plane of $45^{\circ}$. Their coefficients of kinetic friction are $\mu_A = 0.2$ and $\mu_B = 0.3$ respectively. At $t = 0$,both the blocks are at rest and block $A$ is $\sqrt{2} \text{ m}$ behind block $B$. Calculate the time and distance from the initial position where the front faces of the blocks come in line on the inclined plane as shown in the figure. (Use $g = 10 \text{ m/s}^2$)

$A$ block of mass $2 \, kg$ slides down an inclined plane of inclination $30^{\circ}$. The coefficient of friction between the block and the plane is $0.5$. The contact force between the block and the plane is:

In the 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 a coefficient of friction $\mu$,and the mass $m$ is hanging vertically. The pulley is frictionless. Choose the correct statement$(s)$.

$A$ cylindrical vessel filled with water is released on an inclined surface of angle $\theta$ as shown in the figure. The friction coefficient of the surface with the vessel is $\mu (< \tan \theta)$. Then the contact angle made by the surface of water with the incline will be