Q. A simple pendulum is oscillating with amplitude A and angular frequency $\omega$. At displacement $x$ from mean position, the ratio of kinetic energy to potential energy is

1. $\frac{x^2}{A^2-x^2}$
2. $\frac{x^2-A^2}{x^2}$
3. $\frac{A^2-x^2}{x^2}$
4. $\frac{A-x}{x}$

Q. The length and diameter of a metal wire is doubled. The fundamental frequency of vibration will change from n to_______. (tension being kept constant and material of both the wires is same)

1. $\frac{n}{4}$
2. $\frac{n}{16}$
3. $\frac{n}{12}$
4. $\frac{n}{2}$

Q. A mass is suspended from a spring having spring constant k is displaced vertically and released, it oscillates with period T. The weight of the mass suspended is _________. (g = gravitational acceleration)

1. $\frac{k{T}^{2}g}{4{\pi }^2}$
2. $\frac{kTg}{4{\pi }^2}$
3. $\frac{kTg}{2{\pi }^2}$
4. $\frac{k{T}^{2}g}{2{\pi }^2}$

Q. The difference in the effective capacity of two similar capacitors when joined in series and then in parallel is $6\mu F$. The capacity of each capacitor is :

1. $4\mu F$
2. $2\mu F$
3. $8\mu F$
4. $16\mu F$

Q. The pitch of the whistle of an engine appears to drop to $\left(\frac{5}{6}\right)th$ of original value when it passes a stationary observer. If the speed of sound in air is $350$ m/s then the speed of engine is

1. 35 m/s
2. 70 m/s
3. 105 m/s
4. 140 m/s

Q. The dimensions of Stefan's constant are

1. $\left[M^{0}L{T}^{-3}{K}^{-4}\right]$
2. $\left[ML{T}^{-3}{K}^{-3}\right]$
3. $\left[M{L}^2{T}^{-3}{K}^{-4}\right]$
4. $\left[M{L}^0{T}^{-3}{K}^{-4}\right]$

Q. A liquid rises to a height of 1.8 cm in a glass capillary A. Another glass capillary B having diameter 90% of capillary A is immersed in the same liquid. The rise of liquid in capillary B is:

1. 1.4 cm
2. 1.8 cm
3. 2.0 cm
4. 2.2 cm

Q. A cord is wound around the circumference of wheel of radius ${}^{\prime }{r}^{\prime }$. The axis of the wheel is horizontal and moment of inertia about it is ${}^{\prime }{l}^{\prime }$. The weight ${}^{\prime }m{g}^{\prime }$ is attached to the end of the cord and falls from rest. After falling through a distance ${}^{\prime }{h}^{\prime }$, the angular velocity of the wheel will be

1. $[mgh{]}^{1/2}$
2. ${\left[\frac{2mgh}{l+m{r}^2}\right]}^{1/2}$
3. ${\left[\frac{mgh}{l+m{r}^2}\right]}^{1/2}$
4. ${\left[\frac{2mgh}{l+2m{r}^2}\right]}^{1/2}$

Q. In a sonometer experiment, the bridge are separated by a fixed distance. The wire which is slightly elastic, emits a tone of tension is increased to 4T, the tone emitted by the wire will be of frequency

1. 2n
2. n
3. Slightly greater than 2n
4. Slightly less than 2n

Q. A toy cart is tied to the end of an unstretched string of length $l$. When revolved, the toy cart moves in horizontal circle with radius $2l$ and time period $T$. If it is speeded until it moves in horizontal circle of radius $3l$ with period $T_1$, relation between $T$ and $T_1$ is______. (Hooke's law is obeyed)

1. $T_1=\frac{2}{\sqrt{3}}T$
2. $T_1=\sqrt{\frac{3}{2}}T$
3. $T_1=\sqrt{\frac{2}{3}}T$
4. $T_1=\frac{\sqrt{3}}{2}T$

Q. Let $g_h$ and $g_d$ be the acceleration due to gravity at height h above the earth's surface and at depth d below the earth's surface respectively. If $g_h=g_d$, then the relation between h and d is

1. $d=h$
2. $d=\frac{h}{2}$
3. $d=\frac{h}{4}$
4. $d=2h$

Q. A particle is executing SHM of periodic time T. The time taken by a particle in moving from mean position to half the maximum displacement is:

1. $\frac{T}{8}$
2. $\frac{T}{12}$
3. $\frac{T}{2}$
4. $\frac{T}{4}$

Q. In the expression for Boyle's law, the product pV has dimension of

1. Impulse
2. Force
3. Energy
4. Momentum

Q. The distances of a point on the screen from two slits in biprism experiment is $1.8\times {10}^{-5}m$ and $1.23\times {10}^{-5}m$. If wavelength of light used is $6000\mathring{A}$, then fringe formed at that point is

1. 9th bright
2. 9th dark
3. 10th bright
4. 10th dark

Q. The equation of the progressive wave is $y=asin2\pi (nt-\frac{x}{5})$. The ratio of maximum particle velocity to wave velocity is

1. $\frac{\pi a}{5}$
2. $\frac{2\pi a}{5}$
3. $\frac{3\pi a}{5}$
4. $\frac{4\pi a}{5}$

Q. A block body radiates heat at temperatures $T_1$ and $T_2(T_2>T_1)$. The frequency corresponding to maximum energy is

1. More at $T_1$
2. More at $T_2$
3. Equal for $T_1$ and $T_2$
4. Independent of $T_1$ and $T_2$

Q. A rope of 1cm in diameter breaks if tension in it exceeds 500N. The maximum tension that may be given to a similar rope of diameter 2cm is

1. $2000N$
2. $1000N$
3. $500N$
4. $250N$

Q. A metal rod of length L, cross-sectional area A, Young's modulus Y and coefficient of linear expansion $\alpha$ is heated to $t^{o}C$. The work that can be performed by the rod when heated is :

1. $\frac{YA\alpha L{t}^2}{2}rad/s$
2. $\frac{YA{\alpha }^{2}L{t}^2}{2}rad/s$
3. $\frac{YA{\alpha }^2{L}^2{t}^2}{2}rad/s$
4. $\frac{YA\alpha Lt}{2}rad/s$

Q. A particle of mass m is moving in a circular path of constant radius r such that centripetal acceleration is varying with time t as $k^{2}r{t}^2$, where k is a constant. The power delivered to the particle by the force acting on it is

1. $m^2{k}^2{r}^2{t}^2$
2. $m{k}^2{r}^{2}t$
3. $m{k}^{2}r{t}^2$
4. $mk{r}^{2}t$

Q.

The difference between angular speed of minute hand and second hand of a clock is:

1. $\frac{59\pi }{900}rad/s$
2. $\frac{59\pi }{1800}rad/s$
3. $\frac{59\pi }{3600}rad/s$
4. $\frac{59\pi }{24000}rad/s$

Q. A particle performs SHM with amplitude 25 cm and period 3s. The minimum time required for it to move between two mean positions is :

1. $0.6$ s
2. $0.2$ s
3. $0.5$ s
4. $0.4$ s

Q. A satellite of mass m is revolving in circular orbit of radius $r$ around the earth. Its angular momentum w.r.t. the centre of its orbit is

1. $(GMmr{)}^{1/2}$
2. $(GM{m}^2{r}^2{)}^{1/2}$
3. $(GM{m}^{2}r{)}^{1/2}$
4. $(G{M}^2{m}^{2}r{)}^{1/2}$

Q. A large number of liquid drops each of radius a area merged to form a single spherical drop of radius b. The energy released in the process is converted into kinetic energy of the big drop formed. The speed of the big drop is _______.

1. ${\left[\frac{6T}{\rho }(\frac{1}{a}-\frac{1}{b})\right]}^{1/2}$
2. ${\left[\frac{\rho }{6T}(\frac{1}{a}-\frac{1}{b})\right]}^{1/2}$
3. ${\left[\frac{6T}{\rho }(\frac{1}{b}-\frac{1}{a})\right]}^{1/2}$
4. ${\left[\frac{\rho }{6T}(\frac{1}{b}-\frac{1}{a})\right]}^{1/2}$

Q. A solid cylinder has mass M, radius R and length l. Its moment of inertia about an axis passing through its center and perpendicular to its own axis is

1. $\frac{2M{R}^2}{3}+\frac{M{l}^2}{12}$
2. $\frac{M{R}^2}{3}+\frac{M{l}^2}{12}$
3. $\frac{3M{R}^2}{4}+\frac{M{l}^2}{12}$
4. $\frac{M{R}^2}{4}+\frac{M{l}^2}{12}$

Q. For Balmer series, wavelength of first line is ${\lambda }_1$ and for Brackett series, wavelength of first line is ${\lambda }_2$, then $\frac{{\lambda }_1}{{\lambda }_2}$ is

1. 0.162
2. 0.081
3. 0.198
4. 0.238

Q. A hollow sphere of mass M and radius R is rotating with angular frequency $\omega$. It suddenly stops rotating and 75% of kinetic energy is converted to heat. If $s$ is the rise in temperature of the sphere is ________.

1. $\frac{R\omega }{4s}$
2. $\frac{R^2{\omega }^2}{4s}$
3. $\frac{R^2{\omega }^2}{2s}$
4. $\frac{R\omega }{2s}$

Q. An open and closed organ pipe have the same length. The ratio of $p^{th}$ mode of frequency of vibration of air in two pipes is

1. $p(2p+1)$
2. $\frac{2p}{2p-1}$
3. $1$
4. $p$

Q. In a pipe opened at both ends, $n_1$ and $n_2$ be the frequencies corresponding to vibrating lengths $l_1$ and $l_2$, respectively. The end correction is

1. $\frac{n_1{l}_1-n_2{l}_2}{2(n_1-n_2)}$
2. $\frac{n_2{l}_2-n_1{l}_1}{2(n_2-n_1)}$
3. $\frac{n_2{l}_2-n_1{l}_1}{2(n_1-n_2)}$
4. $\frac{n_2{l}_2-n_1{l}_1}{(n_2-n_1)}$

Q. Same current is flowing in two AC circuits. First contains only inductance and second contain only capacitance. If frequency of AC is increased for both, the current will

1. increase min both circuits.
2. increase in first circuit and decrease in second.
3. decrease in both circuits.
4. decrease in first circuit and increase in second.

Q. For diamagnetic materials, magnetic susceptibility is

1. Small and negative
2. Small and positive
3. Large and negative
4. Large and positive