Mechanics PYQ — Page 9

A student measured the diameter of a small steel ball using a screw gauge of least count $0.001\mathrm{cm}$. The main scale reading is $5\mathrm{mm}$ and ${25}^{th}$ division of circular scale coincides with reference line. If screw gauge has a zero error of $-0.004\mathrm{cm}$, the correct diameter of the ball is

Which one of the following statements is incorrect?

Two blocks $A$ and $B$ of masses $3m$ and $m$ respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of $A$ and $B$ immediately after the string is cut, are respectively 

A spring of force constant $k$ is cut into lengths of ratio $1:2:3$. They are connected in series and the new force constant is $k'$. If now they are connected in parallel and force constant is $k''$, then$k':k''$ is

A physical quantity of the dimensions of length that can be formed out of $c,G$ and $\frac{{e}^{2}}{4\pi {\epsilon }_{0}}$, where [$c$ is velocity of light, $G$ is universal constant of gravitation, $e$ is charge & ${\epsilon }_{0}$ is permittivity of free space]:

The acceleration due to gravity at a height $1 km$ above the earth is the same as at a depth $d$ below the surface of earth. Then

One end of string of length $l$ is connected to a particle of mass $m$ and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed $v$, the net force on the particle (directed towards center) will be ($T$ represents the tension in the string)

Consider a drop of rain water having mass $1g$ falling from a height of $1\mathrm{km}$. It hits the ground with a speed of $50 m{s}^{-1}$. Take $g$ constant with a value $10 m{s}^{-2}$. The work done by the (i) gravitational force and the (ii) resistive force of air is

A rope is wound around a hollow cylinder of mass $3 kg$ and radius $40 cm.$ What is the angular acceleration of the cylinder if the rope is pulled with a force of $30 N$?

Two discs of same moment of inertia $( I )$ are rotating in same sense about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities ${\omega }_{1}$ and ${\omega }_{2}$. They are brought into contact face to face coinciding the axis of rotation. The expression for loss in energy during this process is

Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time ${t}_{1}$. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time ${t}_{2}$. The time taken by her to walk up on the moving escalator will be

The bulk modulus of a spherical object is $B$. If it is subjected to uniform pressure $p$, the fractional decrease in radius is

A $U$ tube with both ends open to the atmosphere is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of $10\mathrm{mm}$ above the water level on the other side. Meanwhile, the water rises by $65\mathrm{mm}$ from its original level (see diagram). The density of the oil is____$({\rho }_{w}=1000\mathrm{kg} {m}^{-3})$ 

Two astronauts are floating in gravitational free space after having lost contact with their spaceship. The two will:

Which of the following statements are correct? (i) Centre of mass of a body always coincides with the centre of gravity of the body. (ii) Centre of mass of a body is the point at which the total gravitational torque on the body is zero (iii) A couple on a body produce both translational and rotational motion in a body. (iv) Mechanical advantage greater than one means that small effort can be used to lift a large load.

The $x$ and $y$ coordinates of the particle at any time are $x=5t-2{t}^{2}$ and $y=10t$ respectively, where $x$ and $y$ are in meters and $t$ is in seconds. The acceleration of the particle at $t=2 s$ is

Two cars $P$ and $Q$ start from a point at the same time in a straight line and their positions are represented by ${X}_{P}(t)=at+b{t}^{2}$ and ${X}_{Q}(t)=ft-{t}^{2}$. At what time do the cars have the same velocity?

A light rod of length, $l$ has two masses, ${m}_{1}$ and ${m}_{2}$ attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is

Planck's constant $(h)$, speed of light in a vacuum $( c )$ and Newton's gravitational constant $( G )$ are three fundamental constants. Which of the following combinations of these has the dimension of length?

A particle of mass $10g$ moves along a circle of radius $6.4\mathrm{cm}$with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to $8\times {10}^{-4} J$ by the end of the second revolution after the beginning of the motion?

A particle moves from a point $(- 2\hat{i}+5\hat{j})$ to $(4\hat{j}+3\hat{k})$ when a force of $(4\hat{i}+3\hat{j})N$ is applied. How much work has been done by the force?

A disk and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?

A satellite of mass $m$ is orbiting the earth (of radius $R$) at a height $h$ from its surface. The total energy of the satellite in terms of ${g}_{o}$ , the value of acceleration due to gravity at the earth's surface, is

Three liquids of densities, ${\rho }_{1}, {\rho }_{2}$ and ${\rho }_{3}$ (with, ${\rho }_{1}>{\rho }_{2}>{\rho }_{3})$, having the same value of surface tension,$T$ , rise to the same height in three identical capillaries. The angles of contact, ${\theta }_{1}, {\theta }_{2}$ and ${\theta }_{3}$ obey