$A$ person of mass $60\, kg$ is inside a lift of mass $940\, kg$ and presses the button on the control panel. The lift starts moving upwards with an acceleration of $1.0\, m/s^2$. If $g = 10\, m/s^2$,the tension in the supporting cable is .......... $N$.

State whether the following statements are true or false:
$(a)$ $A$ necessary condition for equilibrium is that the acceleration must be zero.
$(b)$ Centripetal force is always in the opposite direction of centrifugal force.
$(c)$ $A$ man is at rest on a perfectly smooth ice surface in the middle of a pond. He can reach the shore by using Newton's first law.
$(d)$ An object is in equilibrium only if it is at rest.

Two fixed frictionless inclined planes making an angle $30^\circ$ and $60^\circ$ with the vertical are shown in the figure. Two blocks $A$ and $B$ are placed on the two planes. What is the relative vertical acceleration of $A$ with respect to $B$?

$A$ car is moving with uniform velocity on a rough horizontal road. Therefore,according to Newton's first law of motion,

At the moment $t=0$, a time-dependent force $F=at$ (where $a$ is a constant equal to $1 \,Ns^{-1}$) is applied to a body of mass $1 \,kg$ resting on a smooth horizontal plane as shown in the figure. If the direction of this force makes an angle $45^{\circ}$ with the horizontal, then the velocity of the body at the moment it leaves the plane is (acceleration due to gravity $=10 \,ms^{-2}$)

$A$ body of mass $2 \ kg$ is acted upon by two forces each of magnitude $1 \ N$ and inclined at $60^{\circ}$ with each other. The acceleration of the body in $m/s^2$ is $[\cos 60^{\circ}=0.5]$