Mechanics PYQ — Page 24

At what distance above and below the surface of the earth a body will have same weight? (Take radius of earth as $R$)

Time periods of oscillation of the same simple pendulum measured using four different measuring clocks were recorded as $4.62 \mathrm{~s}, 4.632 \mathrm{~s}, 4.6 \mathrm{~s}$ and $4.64 \mathrm{~s}$. The arithmetic mean of these readings in correct significant figure is :

A small steel ball is dropped into a long cylinder containing glycerine. Which one of the following is the correct representation of the velocity time graph for the transit of the ball?

For three vectors $\vec{A}=(-x \hat{i}-6 \hat{j}-2 \hat{k}), \vec{B}=(-\hat{i}+4 \hat{j}+3 \hat{k})$ and $\vec{C}=(-8 \hat{i}-\hat{j}+3 \hat{k})$, if $\vec{A} \cdot(\vec{B} \times \vec{C})=0$, then value of $x$ is _________

A simple pendulum doing small oscillations at a place $\mathrm{R}$ height above earth surface has time period of $T_1=4 \mathrm{~s}$. $T_2$ would be it's time period if it is brought to a point which is at a height $2 \mathrm{R}$ from earth surface. Choose the correct relation $[R=$ radius of earth $]$ :

If two vectors $\vec{A}$ and $\vec{B}$ having equal magnitude $R$ are inclined at an angle $\theta$, then

A big drop is formed by coalescing $1000$ small identical drops of water. If ${E}_{1}$ be the total surface energy of $1000$ small drops of water and ${E}_{2}$ be the surface energy of single big drop of water, the ${E}_{1}$ : ${E}_{2}$ is $x:1$, where $x=$________.

The resultant of two vectors $\vec{A}$ and $\vec{B}$ is perpendicular to $\vec{A}$ and its magnitude is half that of $\vec{B}$. The angle between vectors $\vec{A}$ and $\vec{B}$ is ______ $\circ$.

Escape velocity of a body from earth is $11.2\mathrm{km}{s}^{-1}$. If the radius of a planet be one-third the radius of earth and mass be one-sixth that of earth, the escape velocity from the plate is:

A stationary particle breaks into two parts of masses $m_A$ and $m_B$ which move with velocities $v_A$ and $v_B$ respectively. The ratio of their kinetic energies $\left(K_B: K_A\right)$ is :

Correct Bernoulli's equation is (symbols have their usual meaning) :

Consider a disc of mass $5\mathrm{kg}$, radius $2m$, rotating with angular velocity of $10\mathrm{rad}{s}^{-1}$ about an axis perpendicular to the plane of rotation. An identical disc is kept gently over the rotating disc along the same axis. The energy dissipated so that both the discs continue to rotate together without slipping is _________$J$. 

Young's modulus is determined by the equation given by $\mathrm{Y}=49000 \frac{\mathrm{m}}{\mathrm{l}} \frac{\mathrm{dyn}}{\mathrm{cm}^2}$ where $M$ is the mass and $l$ is the extension of wire used in the experiment. Now error in Young modules $(Y)$ is estimated by taking data from $M-l$ plot in graph paper. The smallest scale divisions are $5 \mathrm{~g}$ and $0.02 \mathrm{~cm}$ along load axis and extension axis respectively. If the value of $M$ and $l$ are $500 \mathrm{~g}$ and $2 \mathrm{~cm}$ respectively then percentage error of $Y$ is :

A small ball of mass $M$ and density $\rho$ is dropped in a viscous liquid of density ${\rho }_{0}$. After some time, the ball falls with a constant velocity. What is the viscous force on the ball?

An average force of $125N$ is applied on a machine gun firing bullets each of mass $10g$ at the speed of $250m{s}^{-1}$ to keep it in position. The number of bullets fired per second by the machine gun is :

Given below are two statements: Statement I: Pressure in a reservoir of water is same at all points at the same level of water. Statement II: The pressure applied to enclosed water is transmitted in all directions equally. In the light of the above statements, choose the correct answer from the options given below:

A block of mass $5\mathrm{kg}$ starting from rest pulled up on a smooth incline plane making an angle of $30^{\circ}$ with horizontal with an effective acceleration of $1m{s}^{-2}$. The power delivered by the puling force at $t=10s$ from the start is _____ $W$. [Use $g=10m{s}^{-2}$] (Calculate the nearest integer value)

Two identical particles each of mass $m$ go round a circle of radius $a$ under the action of their mutual gravitational attraction. The angular speed of each particle will be :

The momentum of a body is increased by $50%$. The percentage increase in the kinetic energy of the body is_$_______%.$

Two satellites of masses $m$ and $3m$ revolve around the earth in circular orbits of radii $r&3r$ respectively. The ratio of orbital speeds of the satellites respectively is

At a certain depth $d$ below surface of earth, value of acceleration due to gravity becomes four times that of its value at a height $3R$ above earth surface. Where $R$ is Radius of earth (Take $R=6400\mathrm{km}$). The depth $d$ is equal to

Every planet revolves around the sun in an elliptical orbit : A. The force acting on a planet is inversely proportional to square of distance from sun. B. Force acting on planet is inversely proportional to product of the masses of the planet and the sun. C. The centripetal force acting on the planet is directed away from the sun. D. The square of time period of revolution of planet around sun is directly proportional to cube of semi-major axis of elliptical orbit. Choose the correct answer from the options given below :

The weight of a body at the surface of earth is $18N$. The weight of the body at an altitude of $3200\mathrm{km}$ above the earth's surface is (given, radius of earth ${R}_{e}=6400\mathrm{km}$)

Dimension of $\frac{1}{{\mu }_{0}{\epsilon }_{0}}$ should be equal to