Mechanics PYQ — Page 10

A solid sphere of mass, $m$ and radius, $R$ is rotating about its diameter. A solid cylinder of the same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation $(\frac{{E}_{\mathrm{sphere}}}{{E}_{\mathrm{cylinder}}})$ will be

Two rotating bodies, $A$ and $B$ of masses, $m$ and $2m$ with moments of inertia. ${I}_{A}$ and ${I}_{B}({I}_{B}>{I}_{A})$ have equal kinetic energy of rotation. If, ${L}_{A}$ and ${L}_{B}$ be their angular momenta, respectively, then,

If the velocity of a particle is $\upsilon =At+B{t}^{2}$, where $\text{A}$ and $\text{B}$ are constants, then the distance travelled by it between $\text{1} \text{s}$ and $\text{2} \text{s}$ is:

A particle moves so that its position vector is given by $\vec{r}=cos\omega t \hat{x} +sin\omega t \hat{y}$, where $\omega$ is a constant. Which of the following is true?

A rigid ball of mass, $m$ strikes a rigid wall at ${60}^{o}$ and gets reflected without any loss of speed as shown in the figure below. The value of impulse imparted by the wall on the ball will be 

In the given figure, $a=15m{s}^{-2}$ represents the total acceleration of a particle moving in the clockwise direction in a circle of the radius $R=2.5m$at a given instant of time. The speed of the particle is 

A rectangular film of liquid is extended from $(4 \mathrm{cm}\times 2 \mathrm{cm})$ to $(5 \mathrm{cm}\times 4 \mathrm{cm})$. If the work done is $3\times {10}^{-4} J$, the value of the surface tension of the liquid is

The ratio of escape velocity at earth $({\upsilon }_{e})$ to the escape velocity at a planet $({\upsilon }_{p})$ whose radius and mean density are twice as that of earth is:

A car is negotiating a curved road of radius $\text{R}$. The road is banked at an angle $\theta$. The coefficient of friction between the tyres of the car and the road is ${\mu }_{s}$. The maximum safe velocity on this road is:

If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is:

Starting from the center of the earth having radius, $R$, the variation of $g$ (acceleration due to gravity) is shown by

Two non-mixing liquids of densities $\rho$ and $n\rho (n>1)$ are put in a container. The height of each liquid is $h.$ A solid cylinder of length $\text{L}$ and density $d$ is put in this container. The cylinder floats with its axis vertical and length $pL(p<1)$ in the denser liquid. The density $d$ is equal to:

From a disc of radius $R$ and mass $M$, a circular hole of diameter $R$, whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis, passing through the centre?

A body of mass $1\mathrm{kg}$ begins to move from rest under the action of a time dependent force $\vec{F}=(2t \hat{i}+3{t}^{2} \hat{j})N$, where $\hat{i}$and $\hat{j}$ are unit vectors along x and y axis. What power will be developed by the force at the time t?

At what height from the surface of earth the gravitation potential and the value of g are $-5.4\times {10}^{7 }J k{g}^{-2}$ and $6.0 m {s}^{-2}$ respectively? Take the radius of earth as $6400 km$:

What is the minimum velocity with which a body of mass m must enter a vertical loop of radius $\text{R}$ so that it can complete the loop?

A bullet of mass $10 g$ moving horizontally with a velocity of $400 m {s}^{-1}$ strikes a wooden block of mass $2 kg$ which is suspended by a light inextensible string of length $5 m.$ As a result, the centre of gravity of the block is found to rise a vertical distance of $10 cm.$ The speed of the bullet after it emerges out horizontally from the block will be

Two identical balls $A$ and $B$ having velocities of $0.5m{s}^{-1}$ and $-0.3m{s}^{-1}$, respectively, collide elastically in one dimension. The velocities of $B$ and $A$ after the collision, respectively, will be

A uniform circular disc of radius $\text{50}\text{ cm}$ at rest is free to rotate about an axis which is perpendicular to its plane and passes through its centre. It is subjected to a torque which produces a constant angular acceleration of $2.0 rad {s}^{-2}$. Its net acceleration in $m {s}^{-2}$ at the end of $\text{2.0 s}$ is approximately:

The heart of a man pumps $5$ litres of blood through the arteries per minute at a pressure of $150\mathrm{mm}$ of mercury. If the density of mercury be $13.6\times {10}^{3} kg{m}^{-3}$ and $g=10 m{s}^{-2}$, then the power of heart in watt is:

A particle of mass $m$ is driven by a machine that delivers a constant power $k$ watts. If the particle starts from rest the force on the particle at time $t$ is:

If dimensions of critical velocity, ${v}_{c}$ of a liquid flowing through a tube are expressed as $[{\eta }^{x}{\rho }^{y}{r}^{z}]$, where, $\eta , \rho$ and $r$ are the coefficient of viscosity of liquid, density of liquid and radius of the tube, respectively, then, the values of $x$, $y$ and $\text{z}$ are given by

A force $\vec{F}=\alpha \hat{i}+3\hat{j}+6\hat{k}$ is acting at a point $\vec{r}=2\hat{i}-6\hat{j}-12\hat{k}$ . The value of $\alpha$ for which angular momentum about origin is conserved is:

Two spherical bodies of mass M and 5M and radii R and 2R released in free space with initial separation between their centres equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller body before collision is: