Mechanics PYQ — Page 85

A ball is released from the top of a tower of height $h$ metres. It takes $T$ seconds to reach the ground. What is the position of the ball in $\mathrm{T} / 3$ seconds?

Two masses $m_1=5 \mathrm{~kg}$ and $m_2=4.8 \mathrm{~kg}$ tied to a string are hanging over a light frictionless pulley. What is the acceleration of the masses when lift free to move $\left(\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^2\right)$ 

A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which one of the following will not be affected?

Consider the following two statements: (A) Linear momentum of a system of particles is zero (B) Kinetic energy of a system of particles is zero Then

A rocket with a lift-off mass $3.5 \times 10^4 \mathrm{~kg}$ is blasted upwards with an initial acceleration of $10 \mathrm{~m} / \mathrm{s}^2$. Then the initial thrust of the blast is

A wire suspended vertically from one of its ends is stretched by attaching a weight of $200 \mathrm{~N}$ to the lower end. The weight stretches the wire by $1 \mathrm{~mm}$. Then the elastic energy stored in the wire is

The time period of a satellite of earth is 5 hours. If the separation between the earth and the satellite is increased to 4 times the previous value, the new time period will become

A car, moving with a speed of $50 \mathrm{~km} / \mathrm{hr}$, can be stopped by brakes after at least $6 \mathrm{~m}$. If the same car is moving at a speed of $100 \mathrm{~km} / \mathrm{hr}$, the minimum stopping distance is

A boy playing on the roof of a $10 \mathrm{~m}$ high building throws a ball with a speed of $10 \mathrm{~m} / \mathrm{s}$ at an angle of $30^{\circ}$ with the horizontal. How far from the throwing point will the ball be at the height of $10 \mathrm{~m}$ from the ground? $$ \left[\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2, \sin 30^{\circ}=\frac{1}{2}, \cos 30^{\circ}=\frac{\sqrt{3}}{2}\right] $$

A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads 49 $\mathrm{N}$, when the lift is stationary. If the lift moves downward with an acceleration of $5 \mathrm{~m} / \mathrm{s}^2$, the reading of the spring balance will be

A block of mass $M$ is pulled along a horizontal frictionless surface by a rope of mass $\mathrm{m}$. If a force $\mathrm{P}$ is applied at the free end of the rope, the force exerted by the rope on the block is

Dimension of $\frac{1}{\mu_0 \varepsilon_0}$, where symbols have their usual meaning, are

A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time ' $t$ ' is proportional to

A spring of spring constant $5 \times 10^3 \mathrm{~N} / \mathrm{m}$ is stretched initially by $5 \mathrm{~cm}$ from the unstretched position. Then the work required to stretch it further by another $5 \mathrm{~cm}$ is

Two stones are projected from the top of a cliff $\mathrm{h}$ metres high, with the same speed $\mathrm{u}$, so as to hit the ground at the same spot. If one of the stones is projected at an angle $\theta$ to the horizontal then the $\theta$ equals

Let $\vec{F}$ be the force acting on a particle having position vector $\vec{r}$ and $\vec{T}$ be the torque of this force about the origin. Then

Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity $\overrightarrow{\mathrm{u}}$ and the other from rest with uniform acceleration $\overrightarrow{\mathrm{f}}$. Let $\alpha$ be the angle between their directions of motion. The relative velocity of the second particle w.r.t. the first is least after a time.

The physical quantities not having same dimensions are

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

The length of a simple pendulum executing simple harmonic motion is increased by $21 \%$. The percentage increase in the time period of the pendulum of increased length is

The escape velocity for a body projected vertically upwards from the surface of earth is $11 \mathrm{~km} / \mathrm{s}$. If the body is projected at an angle of $45^{\circ}$ with the vertical, the escape velocity will be

A body travels a distance $s$ in $t$ seconds. It starts from rest and ends at rest. In the first part of the journey, it moves with constant acceleration $\mathrm{f}$ and in the second part with constant retardation $\mathrm{r}$. The value of $\mathrm{t}$ is given by

The co-ordinates of a moving particle at any time ' $t$ ' are given by $x=\alpha t^3$ and $y=\beta t^3$. The speed of the particle at time ' $t$ ' is given by

A horizontal force of $10 \mathrm{~N}$ is necessary to just hold a block stationary against a wall. The co-efficient of friction between the block and the wall is $0.2$. The weight of the block is