$A$ block of mass $25 \ kg$ is pulled along a horizontal surface by a force at an angle $45^{\circ}$ with the horizontal. The friction coefficient between the block and the surface is $0.25$. The block travels at a uniform velocity. The work done by the applied force during a displacement of $5 \ m$ of the block is (in $J$)

$A$ ball of mass $m$ is released from the top of a smooth movable wedge of mass $m$. When the ball collides with the floor,the velocity of the wedge is $v$. Then the maximum height attained by the ball after an elastic collision with the floor is: (Neglect any edge at the lower end of the wedge).

$A$ hockey player is moving northward and suddenly turns westward with the same speed to avoid an opponent. The force that acts on the player is

Fill in the blanks:
$(a)$ The friction acting on both wheels of a moving bicycle is in the ..... direction.
$(b)$ Friction depends on the ........... and ........ of the contact surfaces.
$(c)$ The necessary condition for parking a vehicle on a banked,curved road is ...........
$(d)$ The time rate of change of momentum gives the physical quantity ...........

$A$ uniform wooden stick of mass $1.6 \,kg$ and length $l$ rests in an inclined manner on a smooth, vertical wall of height $h$ < $l$ such that a small portion of the stick extends beyond the wall. The reaction force of the wall on the stick is perpendicular to the stick. The stick makes an angle of $30^{\circ}$ with the wall and the bottom of the stick is on a rough floor. The reaction of the wall on the stick is equal in magnitude to the reaction of the floor on the stick. Find the ratio $h/l$ and the frictional force $f$ at the bottom of the stick. $(g=10 \,m \,s^{-2})$

$A$ particle is projected with a speed $v_0 = \sqrt{gR}$ at the bottom of a hemispherical bowl. The coefficient of friction between the particle and the hemispherical surface is $\mu = 0.5$. Then,the initial acceleration of the particle is: