$A$ parachutist of weight $w$ strikes the ground with his legs fixed and comes to rest with an upward acceleration of magnitude $3g$. The force exerted on him by the ground during landing is:

In the diagram,$BAC$ is a rigid fixed rough wire and angle $BAC$ is $60^o$. $P$ and $Q$ are two identical rings of mass $m$ connected by a light elastic string of natural length $2a$ and elastic constant $k = \frac{mg}{a}$. If $P$ and $Q$ are in equilibrium when $PA = AQ = 3a$,then the least coefficient of friction between the ring and the wire is $\mu$. Find the value of $\mu + \sqrt{3}$.

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 ......... .

$A$ motor car moving with velocity $7 \ m/s$ stops in $10 \ m$ distance when brakes are applied. What is the relation between the resistance force $(R)$ and the weight $(W)$ of the car? (Take value of $g = 9.8 \ m/s^2$)

Write the relation between the coefficient of static friction,kinetic friction,and rolling friction.

$A$ cubical box of side $a$ sitting on a rough table-top is pushed horizontally with a gradually increasing force until the box moves. If the force is applied at a height from the table top which is greater than a critical height $H$,the box topples first. If it is applied at a height less than $H$,the box starts sliding first. Then,the coefficient of friction between the box and the table top is