NEET UG 2005 — Mechanics

Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is $g$ and that on the surface of the new planet is $\mathrm{g}^{\prime}$ then:

A bomb of mass $30 \mathrm{~kg}$ at rest explodes into two pieces of masses $18 \mathrm{~kg}$ and 12 $\mathrm{kg}$. The velocity of $18 \mathrm{~kg}$ mass is $6 \mathrm{~ms}^{-1}$. The kinetic energy of the other mass is:

Two boys are standing at the ends $\mathrm{A}$ and $\mathrm{B}$ of a ground where $\mathrm{AB}=a$. The boy at $\mathrm{B}$ starts running in a direction perpendicular to $\mathrm{AB}$ with velocity $v_1$. The boy at A starts running simultaneously with velocity $v$ and catches the other in time $t$, where $t$ is:

The moment of inertia of a uniform circular disc of radius $R$ and mass $M$ about an axis passing from the edge of the disc and normal to the disc is:

The ratio of the dimension Planck's constant and that of moment of inertia is the dimension of:

If a vector $2 \hat{i}+3 \hat{j}+8 \hat{k}$ is perpendicular to the vector $4 \hat{j}-4 \hat{i}+\alpha \hat{k}$ then the value of $\alpha$ is:

For a satellite in an orbit around the earth, the ratio of kinetic energy to potential energy is:

The circular motion of a particle with constant speed is:

A ball is thrown vertically. It has a speed of $10 \mathrm{~m} / \mathrm{sec}$ when it has reached one half of its maximum height. How high does the ball rise? Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$.

The displacement $x$ of a particle varies with time $t$ as $x=a e^{-a t}+B^{\beta x}$, where $a, b, \alpha$ and $\beta$ are positive constants. The velocity of the particle will:

A stone tied to the end of a string of 1 $\mathrm{m}$ long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revolutions in 44 seconds, what is the magnitude and direction of acceleration of the stone?

Two bodies have their moments of inertia $l$ and $2 l$ respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momenta will be in the ratio:

A force $F$ acting on an object varies with distance $x$ as shown here. The force is in $N$ and $x$ in $\mathrm{m}$. The work done by the force in moving the object $x=0$ to $x=6 \mathrm{~m}$ is: 

If the angle between the vector $\vec{A}$ and $(\vec{B} \times \vec{A}) \cdot \vec{A}$ is $\theta$, the value of the product $(\vec{B} \times \vec{A}) \cdot \vec{A}$ is equal to:

A drum of radius $R$ and mass $M$ rolls down without slipping along an inclined plane of angle $\theta$. The frictional force: