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The potential energy of a system increases if work is done:
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:
A ball moving with velocity $2\text{ m s}^{-1}$ collides head on with another stationary ball of double the mass. If the coefficient of restitution is $0.5$, then their velocities (in $\text{m s}^{-1}$) after collision will be:
The potential energy of a system increases if work is done:
An engine pumps water through a hosepipe. Water passes through the pipe and leaves it with a velocity of $2\text{ m/s}$. The mass per unit length of water in the pipe is $100\text{ kg m}^{-1}$. What is the power of the engine?
A body of mass 1 kg is thrown upwards with a velocity 20 ms$^{-1}$. It momentarily comes to rest after attaining a height of 18 m. How much energy is lost due to air friction? (Take g = 10 ms$^{-2}$)
Resistance of a carbon resistor determined from colour codes is $(22000 \pm 5\%) \Omega$. The colour of third band must be
An engine pumps water continuously through a hose. Water leaves the hose with a velocity $v$ and $m$ is the mass per unit length of the water jet. What is the rate at which kinetic energy is imparted to water?
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? ($g = 10 \text{ m/s}^2$)
The potential energy of a long spring when stretched by 2 cm is $U$. If the spring is stretched by 8 cm, the potential energy stored in it is:
A vehicle travels half the distance with speed $v$ and the remaining distance with speed $2v$. Its average speed is
A force $F = (20 + 10y)$ acts on a particle in the $y$-direction where $F$ is in Newton and $y$ is in metre. The work done by this force to move the particle from $y = 0$ to $y = 1$ m 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 $g = 10 \text{ m/s}^2$)
The force $F$ acting on a particle of mass $m$ is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from zero to $8 \text{ s}$ is: