JEE Main 2003 — Mechanics

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 

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 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

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 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

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

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