Mechanics PYQ — Page 20

$10$ divisions on the main scale of a Vernier calliper coincide with $11$ divisions on the Vernier scale. If each division on the main scale is of $5$ units, the least count of the instrument is :

Three bodies A, B and C have equal kinetic energies and their masses are $400 \mathrm{~g}$. $1.2 \mathrm{~kg}$ and $1.6 \mathrm{~kg}$ respectively. The ratio of their linear momenta is :

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

In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its $4^{\text {th }}$ division coincides exactly with a certain division on main scale. If 50 vernier scale divisions equal to 49 main scale divisions and zero error in the instrument is $0.04 \mathrm{~mm}$ then how many main scale divisions are there in $1 \mathrm{~cm}$ ?

A circular disc reaches from top to bottom of an inclined plane of length $l$. When it slips down the plane, if takes $t \mathrm{~s}$. When it rolls down the plane then it takes $\left(\frac{\alpha}{2}\right)^{1 / 2} t \mathrm{~s}$, where $\alpha$ is _________

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 $g=10m{s}^{-2}$)

A small ball of mass $m$ and density $\rho$ is dropped in a viscous liquid of density $\rho_0$. After sometime, the ball falls with constant velocity. The viscous force on the ball is :

A wooden block, initially at rest on the ground, is pushed by a force which increases linearly with time $t$. Which of the following curve best describes acceleration of the block with time:

A train starting from rest first accelerates uniformly up to a speed of $80 \mathrm{~km} / \mathrm{h}$ for time $t$, then it moves with a constant speed for time $3 t$. The average speed of the train for this duration of journey will be (in $\mathrm{km} / \mathrm{h}$ ) :

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 _______ $\mathrm{kg} \mathrm{m}^2$.

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:

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 heavy box of mass $50 \mathrm{~kg}$ is moving on a horizontal surface. If co-efficient of kinetic friction between the box and horizontal surface is 0.3 then force of kinetic friction is :

A bus moving along a straight highway with speed of $72 \mathrm{~km} / \mathrm{h}$ is brought to halt within $4 s$ after applying the brakes. The distance travelled by the bus during this time (Assume the retardation is uniform) is _____m.

A ring and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of both bodies are identical and the ratio of their kinetic energies is $\frac{7}{x}$, where $x$ is ______.

The dimensional formula of angular impulse is :

A particle moves in a straight line so that its displacement $x$ at any time $t$ is given by $x^2=1+t^2$. Its acceleration at any time $\mathrm{t}$ is $x^{-\mathrm{n}}$ where $\mathrm{n}=$ ___________

The co-ordinates of a particle moving in $x-y$ plane are given by : $x=2+4 \mathrm{t}, y=3 \mathrm{t}+8 \mathrm{t}^2$. The motion of the particle is :

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

Match List - I with List - II.<br><table class="pyq-table"><tbody><tr><td colspan="2" rowspan="1">List - I (Number)</td><td colspan="2" rowspan="1">List - II (Signficant figure)</td></tr><tr><td>(A)</td><td>$1001$</td><td>(I)</td><td>$3$</td></tr><tr><td>(B)</td><td>$010.1$</td><td>(II)</td><td>$4$</td></tr><tr><td>(C)</td><td>$100.100$</td><td>(III)</td><td>$5$</td></tr><tr><td>(D)</td><td>$0.0010010$</td><td>(IV)</td><td>$6$</td></tr></tbody></table>Choose the correct answer from the options given below:

A heavy iron bar, of weight $W$ is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle $\theta$ with the horizontal. The weight experienced by the person 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 :

In hydrogen like system the ratio of coul0mbian force and gravitational force between an electron and a proton is in the order of :

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 _________$J$.