Mechanics PYQ — Page 86

A circular disc $X$ of radius $R$ is made from an iron plate of thickness $t$, and another disc $Y$ of radius $4 \mathrm{R}$ is made from an iron plate of thickness $\frac{\mathrm{t}}{4}$. Then the relation between the moment of inertia $\mathrm{I}_{\mathrm{X}}$ and $\mathrm{I}_{\mathrm{Y}}$ is

Three forces start acting simultaneously on a particle moving with velocity, $\overrightarrow{\mathrm{v}}$. These forces are represented in magnitude and direction by the three sides of a triangle $\mathrm{ABC}$. The particle will now move with velocity 

A marble block of mass $2 \mathrm{~kg}$ lying on ice when given a velocity of $6 \mathrm{~m} / \mathrm{s}$ is stopped by friction in $10 \mathrm{~s}$. Then the coefficient of friction is

A light spring balance hangs from the hook of the other light spring balance and a block of mass M kg hangs from the former one. Then the true statement about the scale reading is

A particle performing uniform circular motion has angular frequency is doubled \& its kinetic energy halved, then the new angular momentum 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 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

Identify the pair whose dimensions are equal

Two identical particles move towards each other with velocity $2 v$ and $v$ respectively. The velocity of centre of mass is

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

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

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

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

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?

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)

Moment of inertia of a circular wire of mass M and radius R about its diameter is

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?

The kinetic energy needed to project a body of mass $m$ from the earth surface (radius $R$ ) to infinity 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 $C$? 

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? 

A particle of mass $m$ moves along line $P C$ with velocity $v$ as shown. What is the angular momentum of the particle about $\mathrm{P} ?$ 

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