Given $m_1 = 4m_2$. The acceleration of $m_1$ is $a$. Find the velocity of $m_2$ at $t = 0.4 \, s$ in $cm/s$.

Two blocks of masses in the ratio $m:n$ are connected by a light inextensible string passing over a frictionless fixed pulley. If the system of the blocks is released from rest,then the acceleration of the centre of mass of the system of the blocks is ($g$ = acceleration due to gravity).

$A$ force $F=t$ is applied to block $A$ as shown in the figure. The force is applied at $t=0$ seconds when the system was at rest and the string was just straight without tension. Which of the following graphs shows the friction force between block $B$ and the horizontal surface as a function of time $t$?

Identify the incorrect statement.

Place a uniform meter scale horizontally on your extended index fingers with the left one at $0.00 \ cm$ and the right one at $90.00 \ cm$. When you attempt to move both fingers slowly towards the center,initially only the left finger slips with respect to the scale and the right finger does not. After some distance,the left finger stops and the right one starts slipping. Then the right finger stops at a distance $x_R$ from the center $(50.00 \ cm)$ of the scale and the left one starts slipping again. This happens because of the difference in the frictional forces on the two fingers. If the coefficients of static and dynamic friction between the fingers and the scale are $0.40$ and $0.32$,respectively,the value of $x_R$ (in $cm$) is:

Fill in the blanks:
$(a)$ If a force of $10\, N$ is applied to an object and it produces an acceleration of $1\, m s^{-2}$,then the mass of the object is ...
$(b)$ According to Newton's first law of motion,no force is required to keep an object moving with ......... velocity.
$(c)$ The apparent weight of an object in a lift accelerating upwards is ......... .