Mechanics PYQ — Page 83

The relation between time $t$ and distance $\mathrm{x}$ is $\mathrm{t}=a \mathrm{x}^2+\mathrm{bx}$ where $\mathrm{a}$ and $\mathrm{b}$ are constants. The acceleration is

The change in the value of $g$ at a height ' $h$ ' above the surface of the earth is the same as at a depth 'd' below the surface of earth. When both ' $d$ ' and ' $h$ ' are much smaller than the radius of earth, then which one of the following is correct?

A block is kept on a frictionless inclined surface with angle of inclination $\alpha$. The incline is given an acceleration a to keep the block stationary. Then a is equal to 

A particle is projected from a point $\mathrm{O}$ with velocity $u$ at an angle of $60^{\circ}$ with the horizontal. When it is moving in a direction at right angles to its direction at $O$, its velocity then is given by

A mass ' $m$ ' moves with a velocity $v$ and collides inelastically with another identical mass. After collision the $1^{\text {st }}$ mass moves with velocity $v / \sqrt{3}$ in a direction perpendicular to the initial direction of motion. Find the speed of the $2^{\text {nd }}$ mass after collision 

Average density of the earth

A body $A$ of mass $M$ while falling vertically downwards under gravity breaks into two parts; a body B of mass $1 / 3 \mathrm{M}$ and a body $\mathrm{C}$ of mass $2 / 3 \mathrm{M}$. The centre of mass of bodies $\mathrm{B}$ and $\mathrm{C}$ taken together shifts compared to that of body $\mathrm{A}$ towards

A parachutist after bailing out falls $50 \mathrm{~m}$ without friction. When parachute opens, it decelerates at $2 \mathrm{~m} / \mathrm{s}^2$. He reaches the ground with a speed of $3 \mathrm{~m} / \mathrm{s}$. At what height, did he bail out?

Out of the following pair, which one does NOT have identical dimensions is

A body of mass $m$ is accelerated uniformly from rest to a speed $v$ in a time $T$. The instantaneous power delivered to the body as a function time is given by

Consider a car moving on a straight road with a speed of $100 \mathrm{~m} / \mathrm{s}$. The distance at which car can be stopped is $\left[\mu_{\mathrm{k}}=0.5\right]$

The moment of inertia of a uniform semicircular disc of mass $M$ and radius $r$ about a line perpendicular to the plane of the disc through the centre is

The block of mass $M$ moving on the frictionless horizontal surface collides with a spring of spring constant $\mathrm{K}$ and compresses it by length $\mathrm{L}$. The maximum momentum of the block after collision is 

A bullet fired into a fixed target loses half of its velocity after penetrating $3 \mathrm{~cm}$. How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?

Two points $A$ and $B$ move from rest along a straight line with constant acceleration $f$ and $f$ ' respectively. If $A$ takes $m$ sec. more than $B$ and describes ' $n$ ' units more than $B$ in acquiring the same speed then

A particle of mass $10 \mathrm{~g}$ is kept on the surface of a uniform sphere of mass $100 \mathrm{~kg}$ and radius $10 \mathrm{~cm}$. Find the work to be done against the gravitational force between them to take the particle far away from the sphere (you may take $\mathrm{G}=6.67 \times 10^{-11} \mathrm{Nm}^2 / \mathrm{kg}^2$ )

If $S$ is stress and $Y$ is Young's modulus of material of a wire, the energy stored in the wire per unit volume is

$A$ and $B$ are two like parallel forces. A couple of moment $\mathrm{H}$ lies in the plane of $A$ and $B$ and is contained with them. The resultant of $A$ and $B$ after combining is displaced through a distance

A 'T' shaped object with dimensions shown in the figure, is lying on a smooth floor. A force $F$ is applied at the point $P$ parallel to $A B$, such that the object has only the translational motion without rotation. Find the location of $P$ with respect to $C$ 

An annular ring with inner and outer radii $R_1$ and $R_2$ is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring, $F_1 / F_2$ is

A spherical ball of mass $20 \mathrm{~kg}$ is stationary at the top of a hill of height $100 \mathrm{~m}$. It rolls down a smooth surface to the ground, then climbs up another hill of height $30 \mathrm{~m}$ and finally rolls down to a horizontal base at a height of $20 \mathrm{~m}$ above the ground. The velocity attained by the ball is

A $20 \mathrm{~cm}$ long capillary tube is dipped in water. The water rises up to $8 \mathrm{~cm}$. If the entire arrangement is put in a freely falling elevator the length of water column in the capillary tube will be

A projectile can have the same range $\mathrm{R}$ for two angles of projection. If $\mathrm{t}_1$ and $\mathrm{t}_2$ be the times of flights in the two cases, then the product of the two time of flights is proportional to

A particle is moving eastwards with a velocity of $5 \mathrm{~m} / \mathrm{s}$ in 10 seconds the velocity changes to $5 \mathrm{~m} / \mathrm{s}$ northwards. The average acceleration in this time is