Mechanics PYQ — Page 16

The angle between vector $\vec{Q}$ and the resultant of $(2 \vec{Q}+2 \vec{P})$ and $(2 \vec{Q}-2 \vec{P})$ is :

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 :

An astronaut takes a ball of mass $m$ from earth to space. He throws the ball into a circular orbit about earth at an altitude of $318.5 \mathrm{~km}$. From earth's surface to the orbit, the change in total mechanical energy of the ball is $x \frac{\mathrm{GM}_{\mathrm{e}} \mathrm{m}}{21 \mathrm{R}_{\mathrm{e}}}$. The value of $x$ is (take $\left.\mathrm{R}_{\mathrm{e}}=6370 \mathrm{~km}\right)$ :

A $90 \mathrm{~kg}$ body placed at $2 \mathrm{R}$ distance from surface of earth experiences gravitational pull of : $\text { ( } \mathrm{R}=\text { Radius of earth, } \mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2} \text { ) }$

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?

A particle moves in a circle of radius R with constant angular velocity ω. If the centripetal acceleration is 4 m/s² when R = 2 m, what is the angular velocity?

A particle moving in a straight line covers half the distance with speed $6 \mathrm{~m} / \mathrm{s}$. The other half is covered in two equal time intervals with speeds $9 \mathrm{~m} / \mathrm{s}$ and $15 \mathrm{~m} / \mathrm{s}$ respectively. The average speed of the particle during the motion is :

A cylinder is rolling down on an inclined plane of inclination $60^{\circ}$. Its acceleration during rolling down will be $\frac{x}{\sqrt{3}}m{s}^{-2}$, where $x=$ _______(use $g=10m{s}^{-2}$).

The mass of the moon is $\frac{1}{144}$ times the mass of a planet and its diameter $\frac{1}{16}$ times the diameter of a planet. If the escape velocity on the planet is v, the escape velocity on the moon will be:

A particle moves in $x-y$ plane under the influence of a force $\vec{F}$ such that its linear momentum is $\overrightarrow{\mathrm{p}}(\mathrm{t})=\hat{i} \cos (\mathrm{kt})-\hat{j} \sin (\mathrm{kt})$. If $\mathrm{k}$ is constant, the angle between $\overrightarrow{\mathrm{F}}$ and $\overrightarrow{\mathrm{p}}$ will be :

The radius $(r)$, length $(l)$ and resistance $(R)$ of a metal wire was measured in the laboratory as<br>$r=(0.35\pm 0.05)\mathrm{cm}$, $R=(100\pm 10)\mathrm{ohm}$, $l=(15\pm 0.2)\mathrm{cm}$<br>The percentage error in resistivity of the material of the wire is :

The radius $(r)$, length $(l)$ and resistance $(R)$ of a metal wire was measured in the laboratory as $r=(0.35\pm 0.05)\mathrm{cm}$, $R=(100\pm 10)\mathrm{ohm}$, $l=(15\pm 0.2)\mathrm{cm}$ The percentage error in resistivity of the material of the wire is :

The potential energy function (in $J$ ) of a particle in a region of space is given as $U=(2{x}^{2}+3{y}^{3}+2z)$. Here $x,y$ and $z$ are in meter. The magnitude of $x$ - component of force (in $N$ ) acting on the particle at point $P(1,2,3)m$ is:

In an expression $a \times 10^{\mathrm{b}}$;

A ball of mass $0.5\mathrm{kg}$ is attached to a string of length $50\mathrm{cm}$. The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is $400N$. The maximum possible value of angular velocity of the ball in $\mathrm{rad}{s}^{-1}$ is,:

Two discs of moment of inertia ${I}_{1}=4\mathrm{kg}{m}^{2}$ and ${I}_{2}=2\mathrm{kg}{m}^{2}$ about their central axes & normal to their planes, rotating with angular speeds $10\mathrm{rad}{s}^{-1}&4\mathrm{rad}{s}^{-1}$ respectively are brought into contact face to face with their axe of rotation coincident. The loss in kinetic energy of the system in the process is _________$J$.

Pressure inside a soap bubble is greater than the pressure outside by an amount : (given : $\mathrm{R}=$ Radius of bubble $\mathrm{S}=$ Surface tension of bubble)

Train A is moving along two parallel rail tracks towards north with $72\mathrm{km}{h}^{-1}$ and train $B$ is moving towards south with speed $108\mathrm{km}{h}^{-1}$. Velocity of train $B$ with respect to $A$ and velocity of ground with respect to $B$ are (in $m{s}^{-1}$):

Given below are two statements : Statement I : The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well. Statement II : The rise of a liquid in a capillary tube does not depend on the inner radius of the tube. In the light of the above statements, choose the correct answer from the options given below:

A block of mass $m$ is placed on a surface having vertical cross section given by $y=\frac{{x}^{2}}{4}$. If coefficient of friction is $0.5$, the maximum height above the ground at which block can be placed without slipping is:

The bob of a pendulum was released from a horizontal position. The length of the pendulum is $10m$. If it dissipates $10%$ of its initial energy against air resistance, the speed with which the bob arrives at the lowest point is: [Use, $g=10m{s}^{-2}$ ]

A body of mass $1000\mathrm{kg}$ is moving horizontally with a velocity $6m{s}^{-1}$. If $200\mathrm{kg}$ extra mass is added, the final velocity (in $m{s}^{-1}$) is:

A spherical ball of radius $1 \times 10^{-4} \mathrm{~m}$ and density $10^5 \mathrm{~kg} / \mathrm{m}^3$ falls freely under gravity through a distance $h$ before entering a tank of water, If after entering in water the velocity of the ball does not change, then the value of $h$ is approximately: (The coefficient of viscosity of water is $9.8 \times 10^{-6} \mathrm{~N} \mathrm{~s} / \mathrm{m}^2$ )

If average depth of an ocean is $4000m$ and the bulk modulus of water is $2\times {10}^{9}N{m}^{-2}$, then fractional compression $\frac{\Delta V}{V}$ of water at the bottom of ocean is $\alpha \times {10}^{-2}$. The value of $\alpha$ is _______, (Given, $g=10m{s}^{-2},\rho =1000\mathrm{kg}{m}^{-3}$)