NEET UG 2006 — Mechanics

A $0.5 \mathrm{~kg}$ ball moving with a speed of 12 $\mathrm{m} / \mathrm{s}$ strikes a hard wall at an angle of $30^{\circ}$ with the wall. It is reflected with the same speed at the same angle. If the ball is in contact with the wall for 0.25 seconds, the average force acting on the wall is: 

A body of mass $3 \mathrm{~kg}$ is under a constant force which causes a displacement $s$ in metres in it, given by the relation $s=\frac{1}{3} t^2$, where $t$ is in seconds. Work done by the force in 2 seconds is:

A car runs at a constant speed on a circular track of radius $100 \mathrm{~m}$, taking 62.8 seconds for every circular lap. The average velocity and average speed for each circular lap respectively is:

A particle moves along a straight line $\mathrm{OX}$. At a time $t$ (in seconds) the distance $x$ (in metres) of the particle from $\mathrm{O}$ is given by $x=40+12 t-t^3$. How long would the particle travel before coming to rest ?

A rectangular block of mass $m$ and area of cross-section A floats in a liquid of density $\rho$. If it is given a small vertical displacement from equilibrium it undergoes with a time period $T$, Then:

A tube of length $L$ is filled completely with an incompressible liquid of mass $M$ and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity $\omega$. The force exerted by the liquid at the other end is:

A uniform rod of length $l$ and mass $m$ is free to rotate in a vertical plane about $\mathrm{A}$. The rod initially in horizontal position is released. The initial angular acceleration of the rod is (moment of inertia of the rod about $\mathrm{A}$ is $\frac{m l^2}{3}$ ). 

For angles of projection of projectile at angle $\left(45^{\circ}-\theta\right)$ and $\left(45^{\circ}+\theta\right)$, the horizontal range described by the projectile are in the ratio of:

$300 \mathrm{~J}$ of work is done in sliding a $2 \mathrm{~kg}$ block up an inclined plane of height 10 $\mathrm{m}$. Taking $g=10 \mathrm{~m} / \mathrm{s}^2$, work done against friction is:

The Earth is assumed to be a sphere of radius $R$. A platform is arranged at a height $R$ from the surface of the Earth. The escape velocity of a body from this platform is $f v$, where $v$ is its escape velocity from the surface of the Earth. The value of $f$ is:

The moment of inertia of a uniform circular disc of radius $R$ and mass $M$ about an axis touching the disc at its diameter and normal to the disc:

The potential energy of a long spring when stretched by $2 \mathrm{~cm}$ is $U$. If the spring is stretched by $8 \mathrm{~cm}$ the potential energy stored in it is:

The vectors $\vec{A}$ and $\vec{B}$ are such that $|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$. The angle between the two vectors is:

The velocity $v$ of a particle at time $t$ is given by $v=a t+\frac{b}{t+c}$, where $a, b$ and $c$ are constants. The dimensions of $a, b$ and $c$ are:

Two bodies $\mathrm{A}$ (of mass $1 \mathrm{~kg}$ ) and $\mathrm{B}$ (of mass $3 \mathrm{~kg}$ ) are dropped from heights of $16 \mathrm{~m}$ and $25 \mathrm{~m}$, respectively. The ratio of the time taken by them to reach the ground is: