Mechanics PYQ — Page 16

If a rubber ball falls from a height $h$ and rebounds upto the height of $h / 2$. The percentage loss of total energy of the initial system as well as velocity ball before it strikes the ground, respectively, are :

A body is moving unidirectionally under the influence of a constant power source. Its displacement in time $\mathrm{t}$ is proportional to :

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 : $\text { ( } \mathrm{R}=\text { Radius of earth, } \mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2} \text { ) }$

The measured value of the length of a simple pendulum is $20\mathrm{cm}$ with $2\mathrm{mm}$ accuracy. The time for $50$ oscillations was measured to be $40$ seconds with $1$ second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is $N%$. The value of $N$ is:

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?

Two bodies of mass $4g$ and $25g$ are moving with equal kinetic energies. The ratio of magnitude of their linear momentum is :

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 :

The de-Broglie wavelength associated with a particle of mass $m$ and energy $E$ is $h / \sqrt{2 m E}$. The dimensional formula for Planck's constant is :

A cyclist starts from the point $P$ of a circular ground of radius $2 \mathrm{~km}$ and travels along its circumference to the point $\mathrm{S}$. The displacement of a cyclist is: 

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 :

Three balls of masses $2 \mathrm{~kg}, 4 \mathrm{~kg}$ and $6 \mathrm{~kg}$ respectively are arranged at centre of the edges of an equilateral triangle of side $2 \mathrm{~m}$. The moment of intertia of the system about an axis through the centroid and perpendicular to the plane of triangle, will be _______ $\mathrm{kg} \mathrm{m}^2$.

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

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 _________$J$.

Two cars are travelling towards each other at speed of $20 \mathrm{~m} \mathrm{~s}^{-1}$ each. When the cars are $300 \mathrm{~m}$ apart, both the drivers apply brakes and the cars retard at the rate of $2 \mathrm{~m} \mathrm{~s}^{-2}$. The distance between them when they come to rest is :

If $50$ Vernier divisions are equal to $49$ main scale divisions of a travelling microscope and one smallest reading of main scale is $0.5\mathrm{mm}$ the Vernier constant of travelling microscope is:

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)

A particle is moving in a circle of radius $50\mathrm{cm}$ in such a way that at any instant the normal and tangential components of its acceleration are equal. If its speed at $t=0$ is $4m{s}^{-1}$, the time taken to complete the first revolution will be $\frac{1}{\alpha }[1-{e}^{-2\pi }]s$, where $\alpha =$______.

A simple pendulum of length $1m$ has a wooden bob of mass $1\mathrm{kg}$. It is struck by a bullet of mass ${10}^{-2}\mathrm{kg}$ moving with a speed of $2\times {10}^{2}m{s}^{-1}$. The bullet gets embedded into the bob. The height to which the bob rises before swinging back is. (use $g=10m{s}^{-2}$)

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: