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300 J of work is done in sliding a 2 kg block up an inclined plane of height 10 m. Taking g = 10 m/s², work done against friction is:
Copper of fixed volume $V$ is drawn into a wire of length $l$. When this wire is subjected to a constant force $F$, the extension produced in the wire is $\Delta l$. Which of the following graphs is a straight line?
The amount of elastic potential energy per unit volume (in SI unit) of a steel wire of length $100\text{ cm}$ to stretch it by $1\text{ mm}$ is: (given: Young's modulus of the wire $Y = 2.0 \times 10^{11}\text{ N/m}^2$)
A steel wire can withstand a load up to $2940 \text{ N}$. A load of $150 \text{ kg}$ is suspended from a rigid support. The maximum angle through which the wire can be displaced from the mean position, so that the wire does not break when the load passes through the position of equilibrium, is (2008 E)
The Young's modulus of steel is twice that of brass. Two wires of the same length and of the same area of cross-section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weight added to the steel and brass wires must be in the ratio of:
A mass $m$ is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when:
A particle is moving such that its position coordinates $(x, y)$ are $(2\text{ m}, 3\text{ m})$ at time $t = 0$, $(6\text{ m}, 7\text{ m})$ at time $t = 2\text{ s}$ and $(13\text{ m}, 14\text{ m})$ at time $t = 5\text{ s}$. Average velocity vector ($\mathbf{v}_{av}$) from $t = 0$ to $t = 5\text{ s}$ is:
A particle of mass $10 \text{ g}$ moves along a circle of radius $6.4 \text{ cm}$ with a constant tangential acceleration. What is the magnitude of this acceleration, if the kinetic energy of the particle becomes equal to $8 \times 10^{-4} \text{ J}$ by the end of the second revolution after the beginning of the motion?
A particle has an initial velocity $(2\hat{i} + 3\hat{j})$ and an acceleration $(0.3\hat{i} + 0.2\hat{j})$. The magnitude of velocity after $10 \text{ s}$ will be:
A projectile is fired from the surface of the earth with a velocity of $5 \text{ m/s}$ and angle $\theta$ with the horizontal. Another projectile fired from another planet with a velocity of $3 \text{ m/s}$ at the same angle follows a trajectory, which is identical to the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet (in $\text{m/s}^2$) is: [Given, $g = 9.8 \text{ m/s}^2$]
A block of mass $10 \text{ kg}$, moving in the $x$-direction with a constant speed of $10 \text{ m/s}$, is subjected to a retarding force $F = 0.1x \text{ J/m}$ during its travel from $x = 20 \text{ m}$ to $30 \text{ m}$. Its final kinetic energy will be:
A missile is fired for maximum range with an initial velocity of $20 \text{ m/s}$. If $g=10 \text{ m/s}^2$, the range of the missile is:
Two points are located at a distance of $10 \text{ m}$ and $15 \text{ m}$ from the source of oscillation. The period of oscillation is $0.05 \text{ s}$ and the velocity of the wave is $300 \text{ m/s}$. What is the phase difference between the oscillations of two points?
A particle moves in the x-y plane according to rule $x = a \sin \omega t$ and $y = a \cos \omega t$. The particle follows:
The speed of a projectile at its maximum height is half of its initial speed. The angle of projection is:
Consider a drop of rainwater having a mass of $1\text{ g}$ falling from a height of $1\text{ km}$. It hits the ground with a speed of $50\text{ m/s}$. Take $g$ as constant with a value $10\text{ m/s}^2$. The work done by the (i) gravitational force and the (ii) resistive force of air is:
The position vector of a particle $\vec{R}$ as a function of time $t$ is given by: $\vec{R} = 4\sin(2\pi t)\hat{i} + 4\cos(2\pi t)\hat{j}$, where $R$ is in meters, $t$ is in seconds and $\hat{i}, \hat{j}$ denote unit vectors along x and y-directions, respectively. Which one of the following statements is **wrong** for the motion of the particle?
A body of mass $4m$ is lying in the $xy$-plane at rest. It suddenly explodes into three pieces. Two pieces each of mass $m$ move perpendicular to each other with equal speeds $v$. The total kinetic energy generated due to the explosion is:
Two particles A and B move with constant velocities $\mathbf{v}_1$ and $\mathbf{v}_2$. At the initial moment, their position vectors are $\mathbf{r}_1$ and $\mathbf{r}_2$ respectively. The condition for particles A and B for their collision is:
The wave described by $y = 0.25\sin(10\pi x - 2\pi t)$, where $x$ and $y$ are in metres and $t$ in seconds, is a wave traveling along the: