Question Bank Directory

Let a wire be suspended from the ceiling (rigid support) and stretched by a weight $W$ attached at its free end. The longitudinal stress at any point of the cross-sectional area $A$ of the wire is:

A particle has initial velocity $(3\hat{i}+4\hat{j})$ and has acceleration $(0.4\hat{i}+0.3\hat{j})$. Its speed after $10 \text{ s}$ is:

A man weighing 80 kg is standing in a trolley weighing 320 kg. The trolley is resting on frictionless horizontal rails. If the man starts walking on the trolley with a speed of 1 m/s, then after 4 s his displacement relative to the ground will be:

A wire of length $L$ and radius $r$ ($r \ll L$) is kept floating on the surface of a liquid of density $\rho$. The maximum radius of the wire for which it may not sink is: (the surface tension of liquid is $T$)

The velocity of a projectile at the initial point $A$ is $(2\hat{i} + 3\hat{j}) \text{ m/s}$. Its velocity (in m/s) at point $B$ (the point where it hits the ground at the same horizontal level) is:

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 floats with its axis vertical and length $L$. The length of the cylinder inside the denser liquid is $pL$ ($p<1$). The density of the cylinder is $d$. The density $d$ is equal to:

A particle moving with uniform speed in a circular path maintains:

A missile is fired for a maximum range with an initial velocity of $20 \text{ m/s}$. If $g=10 \text{ m/s}^2$, then the range of the missile will be:

Two trains, each $50 \text{ m}$ long, are travelling in the opposite direction with velocities $10 \text{ m/s}$ and $15 \text{ m/s}$. The time of crossing is:

The height $y$ and the distance $x$ along the vertical plane of a projectile on a certain planet (with no surrounding atmosphere) are given by $y = (8t - 5t^2)$ meter and $x = 6t$ meter, where $t$ is in second. The velocity with which the projectile is projected is:

A particle (A) is dropped from a height and another particle (B) is thrown in the horizontal direction with a speed of 5 m/sec from the same height. The correct statement is:

If a body A of mass $M$ is thrown with a velocity $v$ at an angle of $30^{\circ}$ to the horizontal and another body B of the same mass is thrown with the same speed at an angle of $60^{\circ}$ to the horizontal. The ratio of horizontal range of A to B will be:

An electric fan has blades of length $30\text{ cm}$ as measured from the axis of rotation. If the fan is rotating at $1200\text{ r.p.m}$, the acceleration of a point on the tip of the blade is about:

For a prism, when the light undergoes minimum deviation, the relationship between the angle of incidence ($i$) and the angle of emergence ($i'$) is:

Two bullets are fired horizontally and simultaneously towards each other from the rooftops of two buildings (building being $100 \text{ m}$ apart and being of the same height of $200 \text{ m}$) with the same velocity of $25 \text{ m/s}$. When and where will the two bullets collide? ($g=10 \text{ m/s}^2$)

The range of a particle when launched at an angle of $15^\circ$ with the horizontal is $1.5\text{ km}$. What is the range of the projectile when launched at an angle of $45^\circ$ to the horizontal?

A particle starts its motion from rest under the action of a constant force. If the distance covered in the first 10 s is S₁ and that covered in the first 20 s is S₂, then:

The fundamental frequency of a closed organ pipe of a length $20 \text{ cm}$ is equal to the second overtone of an organ pipe open at both ends. The length of the organ pipe open at both ends will be:

The displacement of a particle as a function of time is shown in the figure. The figure shows that

A siren emitting a sound of frequency $800\text{ Hz}$ moves away from an observer towards a cliff at a speed of $15\text{ ms}^{-1}$. The frequency of sound that the observer hears in the echo reflected from the cliff will be: (Take, velocity of sound in air = $330\text{ ms}^{-1}$)