$A$ particle of mass $m$ is executing uniform circular motion on a path of radius $r$. If $p$ is the magnitude of its linear momentum,then the radial force acting on the particle is:

$A$ body of mass $1 \, kg$ starts moving from rest at $t = 0$ in a circular path of radius $8 \, m$. Its kinetic energy varies as a function of time as: $K.E. = 2t^2 \, J$,where $t$ is in seconds. Then:

$A$ man wants to reach from $A$ to the opposite corner of the square $C$. The sides of the square are $100\, m$. $A$ central square of $50\, m \times 50\, m$ is filled with sand. Outside this square,he can walk at a speed of $1\, m/s$. In the central square,he can walk only at a speed of $v\, m/s$ $(v < 1)$. What is the smallest value of $v$ for which he can reach faster via a straight path through the sand than any path in the square outside the sand?

$A$ projectile is fired at an angle of $45^o$ with an initial kinetic energy $K$. What is the kinetic energy of the projectile at its maximum height?

Two projectiles $A$ and $B$ are thrown with the same speed but at angles of $40^{\circ}$ and $50^{\circ}$ with the horizontal,respectively. Then:

Two balls are thrown simultaneously from the ground with the same velocity of $10\,m/s$ but at different angles of projection with the horizontal. Both balls fall at the same distance $5\sqrt{3}\,m$ from the point of projection. What is the time interval between the balls striking the ground?