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A body moves a distance of $10 \text{ m}$ along a straight line under the action of a force of $5 \text{ N}$. If the work done is $25 \text{ joules}$, the angle which the force makes with the direction of motion of the body is:
A particle moves under the effect of a force $F = Cx$ from $x = 0$ to $x = x_1$. The work done in the process is:
A particle moves from position $\vec{r}_1= 3\hat{i}+2\hat{j}-6\hat{k}$ to position $\vec{r}_2=14\hat{i}+13\hat{j}+9\hat{k}$ under the action of force $4\hat{i}+\hat{j}+3\hat{k} \text{ N}$. The work done will be:
Which one of the following is not a conservative force?
Which one of the following statements is true?
What is the minimum velocity with which a body of mass $m$ must enter a vertical loop of radius $R$ so that it can complete the loop?
A particle of mass $m$ is driven by a machine that delivers a constant power of $k$ watts. If the particle starts from rest, the force on the particle at the time $t$ is:
A mass $m$ (moving along the $x$-axis) with velocity $v$ collides and sticks to a mass of $3m$ moving vertically upward (along the $y$-axis) with velocity $2v$. The final velocity of the combination is:
The potential energy of a system increases if work is done:
Resistance of a carbon resistor determined from colour codes is $(22000 \pm 5\%) \Omega$. The colour of third band must be
Water falls from a height of 60 m at a rate of 15 kg/s to operate a turbine. The losses due to frictional forces are 10% of energy. How much power is generated by the turbine? ($g = 10 \text{ m/s}^2$)
A vehicle travels half the distance with speed $v$ and the remaining distance with speed $2v$. Its average speed is
A shell of mass $200\text{ g}$ is ejected from a gun of mass $4\text{ kg}$ by an explosion that generates $1.05\text{ kJ}$ of energy. The initial velocity of the shell is:
A particle moves from a point $(-2\hat i+5\hat j)$ to $(4\hat j+3\hat k)$ when a force of $(4\hat i+3\hat j)$ N is applied. How much work has been done by the force?
What is the minimum velocity with which a body of mass $m$ must enter a vertical loop of radius $R$ so that it can complete the loop?
A body of mass $1 \text{ kg}$ begins to move under the action of a time-dependent force $\vec{F} = (2t\hat{i} + 3t^2\hat{j}) \text{ N}$, where $\hat{i}$ and $\hat{j}$ are unit vectors along the X and Y axes. What power will be developed by the force at time $t$?
A ball is thrown vertically downwards from a height of $20 \text{ m}$ with an initial velocity $v_0$. It collides with the ground, loses $50\%$ of its energy in a collision and rebounds to the same height. The initial velocity $v_0$ is: (Take $g = 10 \text{ m/s}^2$)
On a frictionless surface, a block of mass $M$ moving at speed $v$ collides elastically with another block of same mass $M$ which is initially at rest. After collision the first block moves at an angle $\theta$ to its initial direction and has a speed $v/3$. The second block's speed after the collision is:
An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass $1 \text{ kg}$ moves with a speed of $12 \text{ m s}^{-1}$ and the second part of mass $2 \text{ kg}$ moves with $8 \text{ m s}^{-1}$ speed. If the third part flies off with $4 \text{ m s}^{-1}$ speed, then its mass is:
Two cars moving in opposite directions approach each other with speed of $22 \text{ m/s}$ and $16.5 \text{ m/s}$ respectively. The driver of the first car blows a horn having a frequency $400 \text{ Hz}$. The frequency heard by the driver of the second car is [velocity of sound $340 \text{ m/s}$]