$A$ body of mass $2 \,kg$ thrown vertically from the ground with a velocity of $8 \,ms^{-1}$ reaches a maximum height of $3 \,m$. The work done by the air resistance is (acceleration due to gravity $= 10 \,ms^{-2}$) (in $\,J$)

$A$ particle of mass $M$ moving along the $X$-axis with speed $V_0$ collides with and sticks to another particle of mass $m$ moving along the $Y$-axis with speed $V_0$. What will be the velocity of the combined mass after the collision?

$A$ large block of wood of mass $M = 5.99 \, kg$ is hanging from two long massless cords. $A$ bullet of mass $m = 10 \, g$ is fired into the block and gets embedded in it. The (block $+$ bullet) then swing upwards,their centre of mass rising a vertical distance $h = 9.8 \, cm$ before the (block $+$ bullet) pendulum comes momentarily to rest at the end of its arc. The speed of the bullet just before collision is: (Take $g = 9.8 \, ms^{-2}$) (in $m/s$)

Two particles $P$ and $Q$ each of mass $3m$ lie at rest on the $X$-axis at points $(-a, 0)$ and $(+a, 0)$,respectively. $A$ third particle $R$ of mass $2m$ initially at the origin moves towards the particle $Q$ with velocity $v$. If all the collisions of the system of $3$ particles are elastic and head-on,the total number of collisions in the system is

Explain with illustrations the meaning of work,energy,and power in everyday life and state that this meaning has no relation with the meaning in physics.

$A$ small disk can slide in a circular path on a frictionless inclined plane inclined at an angle of $30^\circ$ with the help of a thread as shown. The mass of the disk is $m$ and the acceleration due to gravity is $g$. If the disk is released when the thread is horizontal,the expression for the tension in the thread at the lowest point is: ................. $mg$