An object of mass $10 \,kg$ is projected from the ground with a speed of $40 \,m/s$ at an angle of $60^{\circ}$ with the horizontal. The rate of change of momentum of the object one second after projection in $SI$ units is ........ [Take $g = 9.8 \,m/s^2$]

Given $m_1 = 4m_2$ and the acceleration of $m_1$ is $a$. How much distance in $cm$ will $m_2$ cover in $0.4 \, s$?

An object of mass $m$ is being moved with a constant velocity under the action of an applied force of $2\, N$ along a frictionless surface with the following surface profile. The correct applied force vs distance graph will be:

$A$ block of mass $15 \;kg$ is placed on a long trolley. The coefficient of static friction between the block and the trolley is $0.18$. The trolley accelerates from rest with $0.5 \;m s^{-2}$ for $20 \;s$ and then moves with uniform velocity. Discuss the motion of the block as viewed by
$(a)$ a stationary observer on the ground,
$(b)$ an observer moving with the trolley.

Two blocks $A$ and $B$ of masses $5 \ kg$ and $10 \ kg$ respectively are placed as shown in the figure. The coefficient of friction between all the surfaces is $0.2$. $A$ force $F$ is applied on block $A$ at an angle of $30^{\circ}$ with the horizontal. If the system moves with constant acceleration,find the acceleration of block $B$. (Assume $g = 10 \ m/s^2$ and $F = 100 \ N$) (in $m/s^2$)

$A$ force of $(2.6 \hat{i} + 1.6 \hat{j}) \text{ N}$ acts on a body of mass $2 \text{ kg}$. If the velocity of the body at time $t = 0$ is $(3.6 \hat{i} - 4.8 \hat{j}) \text{ ms}^{-1}$, the time at which the body will just have a velocity along the $x$-axis only is: (in $\text{ s}$)