NEET UG 2015 — Mechanics

A ball is thrown vertically downwards from a height of $20 m$ with an initial velocity ${v}_{0}$. It collides with the ground, loses $50$ percent of its energy in collision and rebounds to the same height. The initial velocity ${v}_{0}$ is: (Take $g=10 m {s}^{-2}$)

A block of mass $10\mathrm{kg}$, moving in $x$ direction with a constant speed of $10 m {s}^{-1}$ , is subjected to a retarding force $F=[(0.1)x] J{m}^{-1}$ during its travel from $x=20m$ to $30m$ . Its final kinetic energy will be:

A block $\text{A}$ of mass ${m}_{1}$ rests on a horizontal table. A light string connected to it passes over a frictionless pulley at the edge of table and from its other end another block $\text{B}$ of mass ${m}_{2}$ is suspended. The coefficient of kinetic friction between the block and the table is ${\mu }_{k}$. When the block $\text{B}$ is sliding on the table, the tension in string is:

A force $\vec{F}=\alpha \hat{i}+3\hat{j}+6\hat{k}$ is acting at a point $\vec{r}=2\hat{i}-6\hat{j}-12\hat{k}$ . The value of $\alpha$ for which angular momentum about origin is conserved is:

A mass $\text{m}$ moves in a circle on a smooth horizontal plane with velocity ${v}_{0}$ at a radius ${R}_{0}$ . The mass is attached to a string which passes through a smooth hole in plane as shown.  The tension in the string is increased gradually and finally $\text{m}$ moves in a circle of radius $\frac{{R}_{0}}{2}$. The final value of the kinetic energy is:

A particle of mass $m$ is driven by a machine that delivers a constant power $k$ watts. If the particle starts from rest the force on the particle at time $t$ is:

A particle undergoes a one-dimensional motion such that its velocity varies according to $v(x)=\beta {x}^{-2n}$, where $\beta$ and $\text{n}$ are constants and $x$ is the position of the particle. The acceleration of the particle as a function of $x$ is given by

A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches $30^{\circ}$, the box starts to slip and slides $4.0m$ down the plank in $4.0s$. The coefficients of static and kinetic friction between the box and the plank will be, respectively: 

A remote-sensing satellite of earth revolves in a circular orbit at a height of $0.25\times {10}^{6}$ m above the surface of earth. If earth's radius is $6.38\times {10}^{6} m$ and $g=9.8 m {s}^{-2}$, then the orbital speed of the satellite is: Mass of earth undefined

A rod of weight $\text{W}$ is supported by two parallel knife edges $\text{A}$ and $\text{B}$ and is in equilibrium in a horizontal position. The knives are at a distance $\text{d}$ from each other. The centre of mass of the rod is at distance $\text{x}$ from $\text{A}$ . the normal reaction on $\text{A}$ is:

A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then,

A ship $\text{A}$ is moving Westwards with a speed of $10 km{h}^{-1}$ and a ship $\text{B}$ $\text{100 km}$ south of $\text{A}$, is moving Northwards with a speed of $10 km {h}^{-1}$ . The time after which the distance between them becomes shortest, is:

A wind with speed $40m{s}^{-1}$ blows parallel to the roof of a house. The area of the roof is $250 {m}^{2}$ . Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the direction of the force will be : $({\rho }_{\mathrm{air}}=1.2\mathrm{kg}{m}^{-3})$

An automobile moves on a road with a speed of $54 km {h}^{-1}$ . The radius of its wheels is $0.45 \text{m}$ and the moment of inertia of the wheel about its axis of rotation is $3 kg {m}^{2}$ . If the vehicle is brought to rest in $\text{15 s}$, the magnitude of average torque transmitted by its brakes to the wheel is:

If dimensions of critical velocity, ${v}_{c}$ of a liquid flowing through a tube are expressed as $[{\eta }^{x}{\rho }^{y}{r}^{z}]$, where, $\eta , \rho$ and $r$ are the coefficient of viscosity of liquid, density of liquid and radius of the tube, respectively, then, the values of $x$, $y$ and $\text{z}$ are given by

If energy $(E)$, velocity $(V)$ and time $(T)$ are chosen as the fundamental quantities, the dimensional formula of surface tension will be___(For surface tension, Force=Surface tension$\times$length)

If vectors $\vec{A}=\mathrm{cos}⁡\omega t \hat{i}+sin\omega t \hat{j}$ and $\vec{B}=cos\frac{\omega t}{2 }\hat{i}+\mathrm{sin}⁡\frac{\omega t}{2 }\hat{j}$ are functions of time, then the value of $t$ at which they are orthogonal to each other is:

Kepler's third law states that the square of the period of revolution $\text{(T)}$ of a planet around the sun is proportional to the third power of the average distance $\text{r}$ between sun and planet i.e., ${T}^{2}=K{r}^{3}$. Here $\text{K}$ is constant. If the masses of sun and planet are $\text{M}$ and $\text{m}$ respectively then as per Newton's law of gravitation force of attraction between them is $F=\frac{GMm}{{r}^{2}}$, here $\text{G}$ is gravitational constant. The relation between $\text{G}$ and $\text{K}$ is described as:

On a frictionless surfaces, a block of mass $\text{M}$ moving at speed $v$ collides elastically with another block of same mass $\text{M}$ which is initially at rest. After collision the first block moves at an angle $\theta$ to its initial direction and has a speed $\frac{v}{3}$ . The second block's speed after the collision is:

Point masses ${m}_{1}$ and ${m}_{2}$ are placed at the opposite ends of rigid rod of length $\text{L}$, and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point $\text{L}$ on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity ${\omega }_{0}$ is minimum, is given by: 

The approximate depth of an ocean is $\text{2700 m}$ . The compressibility of water is $45.4\times {10}^{-11} P{a}^{-1}$ and density of water is ${10}^{3}$ ${\text{kg/m}}^{3}$. What fractional compression of water will be obtained at the bottom of the ocean ?

The cylindrical tube of a spray pump has radius $R$ , one end of which has $n$ fine holes, each of radius $r$ . If the speed of the liquid in the tube is $V$ , the speed of the ejection of the liquid through the holes is :

The heart of a man pumps $5$ litres of blood through the arteries per minute at a pressure of $150\mathrm{mm}$ of mercury. If the density of mercury be $13.6\times {10}^{3} kg{m}^{-3}$ and $g=10 m{s}^{-2}$, then the power of heart in watt is:

The position vector of a particle $\vec{R}$ as a function of time is given by: $\vec{R}=4\mathrm{sin}⁡(2\pi t)\hat{i}+4cos⁡(2\pi t)\hat{j}$ Where R is in meters, t is in seconds and $\hat{i}$ and $\hat{j}$ denote unit vectors along x- and y-directions, respectively. Which one of the following statements is wrong for the motion of particle?

The value of coefficient of volume expansion of glycerin is $5\times {10}^{-4 }{K}^{-1}$. The fractional change in the density of glycerin for a rise of ${40 }^{o}C$ in its temperature is:

The Young's modulus of steel is twice that of brass. Two wires of same length and of same area of cross-section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weights added to the steel and brass wires must be in the ratio of:

Three blocks A, B and C, of masses $4\mathrm{kg},2\mathrm{kg}$ $1\mathrm{kg}$ and respectively, are in contact on a frictionless surface, as shown. If a force of $14N$ is applied on the$4\mathrm{kg}$ block, then the contact force between A and B is: 

Three identical spherical shells, each of mass $m$ and radius $r$ are placed as shown in the figure. Consider an axis $X{X}^{'}$ which is touching the two shells and passing through the diameter of the third shell. The moment of inertia of the system consisting of these three spherical shells about $X{X}^{'}$ axis is: 

Two particles A and B move with constant velocities ${\vec{v}}_{1}$ and ${\vec{v}}_{2}$. At the initial moment their position vectors are ${\vec{r}}_{1}$ and ${\vec{r}}_{2}$ respectively. The condition for particles A and B for their collision is:

Two particles of masses ${m}_{1}, {m}_{2}$ move with initial velocities ${u}_{1}$ and ${u}_{2}$. On collision, one of the particles get excited to higher level, after absorbing energy $\epsilon .$ If final velocities of particles be ${v}_{1}$ and ${v}_{2}$ then we must have:

Two similar springs $\text{P}$ and $\text{Q}$ have spring constants ${K}_{P}$ and ${K}_{Q}$, such that ${K}_{P}>{K}_{Q}$. They are stretched, first by the same amount (case a), then by the same force (case b). the work done by the springs ${W}_{P}$ and ${W}_{Q}$ are related as respectively, in case

Two spherical bodies of mass M and 5M and radii R and 2R released in free space with initial separation between their centres equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller body before collision is:

Two stones of masses $m$ and $2m$ are whirled in horizontal circles, the heavier one in radius $\frac{r}{2}$ and the lighter one in radius $r$. The tangential speed of lighter stone is $n$ times that of the tangential speed of the heavier stone. They are reported to experience the same centripetal force. The value of $n$ is,

Water rises to a height 'h' in capillary tube. If the length of capillary tube above the surface of water is made less than 'h', then: