Physics Mechanics questions from JEE Main 2002.
A ball whose kinetic energy is E, is projected at an angle of $45^{\circ}$ to the horizontal. The kinetic energy of the ball at the highest point of its flight will be
A bead of weight $w$ can slide on smooth circular wire in a vertical plane. The bead is attached by a light thread to the highest point of the wire and in equilibrium, the thread is taut and make an angle $\theta$ with the vertical then tension of the thread and reaction of the wire on the bead are
A cylinder of height $20 \mathrm{~m}$ is completely filled with water. The velocity of efflux of water (in $\mathrm{ms}^{-1}$ ) through a small hole on the side wall of the cylinder near its bottom is
A lift is moving down with acceleration a. A man in the lift drops a ball inside the lift. The acceleration of the ball as observed by the man in the lift and a man standing stationary on the ground are respectively
A light string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$ (vertically). If the acceleration of the system is $\mathrm{g} / 8$, then the ratio of the masses is
A particle of mass $m$ moves along line $P C$ with velocity $v$ as shown. What is the angular momentum of the particle about $\mathrm{P} ?$ 
A solid sphere, a hallow sphere and a ring are released from top of an inclined plane (frictionless) so that they slide down the plane. Then maximum acceleration down the plane is for (no rolling)
A spring of force constant $800 \mathrm{~N} / \mathrm{m}$ has an extension of $5 \mathrm{~cm}$. The work done is extending it from $5 \mathrm{~cm}$ to $15 \mathrm{~cm}$ is
Energy required to move a body of mass m from an orbit of radius 2R to 3R is
From a building two balls $\mathrm{A}$ and $\mathrm{B}$ are thrown such that $\mathrm{A}$ is thrown upwards $\mathrm{A}$ and $\mathrm{B}$ downwards (both vertically). If $\mathrm{v}_{\mathrm{A}}$ and $\mathrm{v}_{\mathrm{B}}$ are their respective velocities on reaching the ground, then
Identify the pair whose dimensions are equal
If a body looses half of its velocity on penetrating 3 cm in a wooden block, then how much will it penetrate more before coming to rest?
If suddenly the gravitational force of attraction between Earth and a satellite revolving around it becomes zero, then the satellite will
Initial angular velocity of a circular disc of mass $M$ is $\omega_1$. Then two small spheres of mass $m$ are attached gently to diametrically opposite points on the edge of the disc. What is the final angular velocity of the disc?
Moment of inertia of a circular wire of mass M and radius R about its diameter is
One end of a massless rope, which passes over a massless and frictionless pulley $P$ is tied to a hook $C$ while the other end is free. Maximum tension that the rope can bear is $360 \mathrm{~N}$. With what value of maximum safe acceleration (in $\mathrm{ms}^{-2}$ ) can a man of $60 \mathrm{~kg}$ climb on the rope? 
Speeds of two identical cars are $u$ and $4 u$ at the specific instant. The ratio of the respective distances in which the two cars are stopped from that instant is
The escape velocity of a body depends upon mass as
The kinetic energy needed to project a body of mass $m$ from the earth surface (radius $R$ ) to infinity is
The minimum velocity (in $\mathrm{ms}^{-1}$ ) with which a car driver must traverse a flat curve of radius $150 \mathrm{~m}$ and coefficient of friction $0.6$ to avoid skidding is
Three identical blocks of masses $\mathrm{m}=2 \mathrm{~kg}$ are drawn by a force $\mathrm{F}=10.2 \mathrm{~N}$ with an acceleration of $0.6 \mathrm{~ms}^{-2}$ on a frictions surface, then what is the tension (in $\mathrm{N}$ ) in the string between the blocks $B$ and $C$? 
Two forces are such that the sum of their magnitudes is $18 \mathrm{~N}$ and their resultant is $12 \mathrm{~N}$ which is perpendicular to the smaller force. Then the magnitudes of the forces are
Two identical particles move towards each other with velocity $2 v$ and $v$ respectively. The velocity of centre of mass is
When forces $F_1, F_2, F_3$ are acting on a particle of mass $m$ such that $F_2$ and $F_3$ are mutually perpendicular, then the particle remains stationary. If the force $F_1$ is now removed then the acceleration of the particle is