Mechanics PYQ — Page 15

A body is moving with velocity $30 \mathrm{~m} / \mathrm{s}$ towards east. After $10 \mathrm{~s}$ its velocity becomes $40 \mathrm{~m} / \mathrm{s}$ towards north. The average acceleration of the body is

A particle of mass $m$ is thrown upwards from the surface of the earth, with a velocity $u$. The mass and the radius of the earth are, respectively, $M$ and $R . G$ is gravitational constant and $g$ is acceleration due to gravity on the surface of the earth. The minimum value of $u$ so that the particle does not return back to earth, is

The dimensions of $\left(\mu_0 \varepsilon_0\right)^{-1 / 2}$ are

A small mass attached to a string rotates on frictionless table top as shown. If the tension is the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of 2 , the kinetic energy of the mass will 

The moment of inertia of a thin uniform rod of mass $M$ and length $L$ about an axis passing through its mid-point and perpendicular to its length is $I_0$. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is

The potential energy of a system increase if work is done

A mass $m$ moving horizontally (along the $x$-axis) with velocity $v$ collides and sticks to mass of $3 m$ moving vertically upward (along the $y$-axis) with velocity $2 v$. The final velocity of the combination is

A body of mass $M$ hits normally a rigid wall with velocity $y$ and bounces back with the same velocity. The impulse experienced by the body is

A particle of mass $M$ is situated at the centre of spherical shell of mass and radius $a$. The magnitude of the gravitational potential at a point situated at $\frac{a}{2}$ distance from the centre, will be

A particle moves in a circle of radius $5 \mathrm{~cm}$ with constant speed and time period $0.2 \pi \mathrm{s}$. The acceleration of the particle is

A body projected vertically from the earth reaches a height equal to earth's radius before returning to the earth. The power exerted by the gravitational force is greatest

Force $F$ on a particle moving in a straight line varies with distance $d$ as shown in the figure. The work done on the particle during its displacement of $12 \mathrm{~m}$ is 

A boy standing at the top of a tower of $20 \mathrm{~m}$ height drops a stone. Assuming $g=10 \mathrm{~ms}^{-2}$, the velocity with which it hits the ground is

Which one of the following is present as an active ingredient in bleaching powder for bleaching action?

A particle covers half of its total distance with speed $v_1$ and the rest half distance with speed $v_2$. Its average speed during the complete journey is

A conveyor belt is moving at a constant speed of $2 \mathrm{~m} / \mathrm{s}$. A box is gently dropped on it. The coefficient of friction between them is $\mu=0.5$. The distance that the box will move relative to belt before coming to rest on it taking $g=10 \mathrm{~ms}^{-2}$, is

The instantaneous angular position of a point on a rotating wheel is given by the equation $Q(t)=2 t^3-6 t^2$ The torque on the wheel becomes zero at

The additional kinetic energy to be provided to a satellite of mass $m$ revolving around a planet of mass $M$, to transfer it from a circular orbit of radius $R_1$ to another of radius $R_2\left(R_2>R_1\right)$ is

The speed of a projectile at its maximum height is half of its initial speed. The angle of projection is

The radii of circular orbits of two satellites A and $B$ of the earth are $4 R$ and $R$, respectively. If the speed of satellite $A$ is $3 v$, then the speed of satellite $B$ will be

(1) Centre of gravity (CG) of a body is the point at which the weight of the body acts. (2) Centre of mass coincides with the centre of gravity if the earth is assumed to have infinitely large radius. (3) To evaluate the gravitational field intensity due to any body at an external point, the entire mass of the body can be considered to be concentrated at its CG. (4) The radius of gyration of any body rotating about an axis is the length of the perpendicular dropped from the CG of the body to the axis. Which one of the following pairs of statements is correct?

A block of mass $\mathrm{m}$ is in contact with the cart $\mathrm{C}$ as shown in the figure.  The coefficient of static friction between the block and the cart is $\mu$. The acceleration $\alpha$ of the cart that will prevent the block from falling satisfies

From a circular disc of radius $R$ and mass $9 \mathrm{M}$, a small disc of mass $M$ and radius $\frac{R}{3}$ is removed concentrically. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through its centre is

The dependence of acceleration due to gravity $g$ on the distance $r$ from the centre of the earth, assumed to be a sphere of radius $R$ of uniform density is as shown in figures below (1)  (2) (3) (4) The correct figure is