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A mass $m$ slips along the wall of a semispherical surface of radius $R$. The velocity at the bottom of the surface is:

Two bodies $A$ and $B$ of the same mass undergo completely inelastic one-dimensional collision. The body $A$ moves with velocity $v_1$ while the body $B$ is at rest before collision. The velocity of the system after collision is $v_2$. The ratio of $v_1 : v_2$ is:

The object $A$ has half the kinetic energy as that of the object $B$. The object $B$ has half the mass as that of the object $A$. The object $A$ speeds up by $1\text{ ms}^{-1}$ and then has the same kinetic energy as that of the object $B$. The initial speed of the object $A$ is: (Take $\sqrt{2} \cong 1.4$)

A stone tied to a string of length $L$ is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed $u$. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is:

A man pushes a wall and fails to displace it. He does:

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:

The compound that is most difficult to protonate is :

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?