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Let $T_1$ and $T_2$ be the energy of an electron in the first and second excited states of hydrogen atoms, respectively. According to the Bohr's model of an atom, the ratio $T_1 : T_2$ is

A gravitational field is present in a region, and a mass is shifted from $A$ to $B$ through different paths as shown. If $W_1$, $W_2$ and $W_3$ represent the work done by the gravitational force along their respective paths, then:

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 sphere of mass $m$ is tied to the end of a string of length $l$ and rotated through the other end along a horizontal circular path with speed $v$. The work done by the centripetal force in a full horizontal circle is:

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 stone of mass $1 \text{ kg}$ tied to a light inextensible string of length $L = \frac{10}{3} \text{ m}$ is whirling in a circular path of radius $L$ in a vertical plane. If the ratio of the maximum tension in the string to the minimum tension in the string is 4 and if $g$ is taken to be $10 \text{ m/s}^2$, the speed of the stone at the highest point of the circle is:

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

The spring extends by $x$ on loading, then energy stored by the spring is: (if $T$ is the tension in the spring and $k$ is the spring constant)

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:

The potential energy of a certain spring when stretched through a distance 'S' is $10 \text{ joule}$. The amount of work (in joule) that must be done on this spring to stretch it through an additional distance 'S' will be:

Which one of the following is not a conservative force?

A mass of $0.5 \text{ kg}$ moving with a speed of $1.5 \text{ m/s}$ on a horizontal smooth surface, collides with a nearly weightless spring of force constant $k = 50 \text{ N/m}$. The maximum compression of the spring would be:

Which one of the following statements is true?

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?

Which molecule among the following is non-polar?