Physics Mechanics questions from NEET UG 2012.
A car of mass $m$ is moving on a level circular track of radius $R$. If $\mu_s$ represents the static friction between the road and tyres of the car, the maximum speed of the car in circular motion is given by
A car of mass $1000 \mathrm{~kg}$ negotiates a banked curve of radius $90 \mathrm{~m}$ on a frictionless road. If the banking angle is $45^{\circ}$, the speed of the car is
A car of mass $m$ starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude $P_0$. The instantaneous velocity of this car is proportional to
A circular platform is mounted on a frictionless vertical axle. Its radius $R=2 \mathrm{~m}$ and its moment of inertia about the axle is $200 \mathrm{~kg} \mathrm{~m}^2$. It is initially at rest. A $50 \mathrm{~kg}$ man stands on the edge of the platform and begins to walk along the edge at the speed of $1 \mathrm{~ms}^{-1}$ relative to the ground. Time taken by the man to complete one revolution is
A geostationary satellite is orbiting the earth at a height of $5 R$ above that surface of the earth, $R$ being the radius of the earth. The time period of another satellite in hours at a height of $2 R$ from the surface of the earth is
A particle has initial velocity $(2 \mathbf{i}+3 \mathbf{j})$ and acceleration $(0.3 \mathbf{i}+0.2 \mathbf{j})$. The magnitude of velocity after $10 \mathrm{~s}$ will be
A solid cylinder of mass $3 \mathrm{~kg}$ is rolling on a horizontal surface with velocity $4 \mathrm{~ms}^{-1}$. It collides with a horizontal spring of force constant $200 \mathrm{Nm}^{-1}$. The maximum compression produced in the spring will be
A spherical planet has a mass $M_p$ and diameter $D_p$. A particle of mass $m$ falling freely near the surface of this planet will experience an acceleration due to gravity, equal to
A stone is dropped from a height $h$. It hits the ground with a certain momentum $p$. If the same stone is dropped from a height $100 \%$ more than the previous height, the momentum when it hits the ground will change by
If $v_e$ is escape velocity and $v_o$ is orbital velocity of a satellite for orbit close to the Earth's surface, then these are related by
$A B C$ is an equilateral triangle with $O$ as its centre. $\mathrm{F}_1, \mathrm{~F}_2$ and $\mathrm{F}_3$ represent three forces acting along the sides $A B, B C$ and $A C$ respectively. If the total torque about $O$ is zero then the magnitude of $\mathrm{F}_3$ is 
The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are
The dimensions of $\left(\mu_0 \varepsilon_0\right)^{-1 / 2}$ are
The height at which the weight of a body becomes $1 / 16$ th, its weight on the surface of earth (radius $R$ ), is
The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is
The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through 
The motion of a particle along a straight line is described by equation $x=8+12 t-t^3$ where, $x$ is in metre and $t$ in second. The retardation of the particle when its velocity becomes zero, is
The potential energy of a particle in a force field is $U=\frac{A}{r^2}-\frac{B}{r}$, where $A$ and $B$ are positive constants and $r$ is the distance of particle from the centre of the field. For stable equilibrium, the distance of the particle is
Three masses are placed on the $x$-axis : $300 \mathrm{~g}$ at origin, $500 \mathrm{~g}$ at $x=40 \mathrm{~cm}$ and $400 \mathrm{~g}$ at $x=70 \mathrm{~cm}$. The distance of the centre of mass from the origin is
Two persons of masses $55 \mathrm{~kg}$ and $65 \mathrm{~kg}$ respectively, are at the opposite ends of a boat. The length of the boat is $3.0 \mathrm{~m}$ and weighs $100 \mathrm{~kg}$. The $55 \mathrm{~kg}$ man walks up to the $65 \mathrm{~kg}$ man and sits with him. If the boat is in still water the centre of mass of the system shifts by
Two spheres $A$ and $B$ of masses $m_1$ and $m_2$ respectively collide. $A$ is at rest initially and $B$ is moving with velocity $y$ along $x$-axis. After collision $B$ has a velocity $\frac{v}{2}$ in a direction perpendicular to the original direction. The mass $A$ moves after collision in the direction
When a mass is rotating in a plane about a fixed point, its angular momentum is directed along
Which one of the following plots represents the variation of gravitational field on a particle with distance $r$ due to a thin spherical shell of radius $R$ ? ( $r$ is measured from the centre of the spherical shell).