Q. The equation of sound wave is $y=0.0015sin(62.4x+316t)$. Find the wavelength of this wave :

1. $0.2$ unit
2. $0.1$ unit
3. $0.3$ unit
4. none of these

Q. In Young's double slit experiment if the slit widths are in the ratio $1:9$. The ratio of the intensity at minima to that at maxima will be :

1. $1$
2. $\frac{1}{9}$
3. $\frac{1}{4}$
4. $\frac{1}{3}$

Q. If the density of a small planet is the same as that of earth, while the radius of the planet is $0.2$ times that the earth, the gravitational acceleration on the surface of that planet is:

1. $0.2$ g
2. $0.4$ g
3. $2$ g
4. $4$ g

Q. Two springs have spring constant $k_A$ and $k_B$ and $k_A>k_B$. The work required to stretch them by same extension will be:

1. more in spring A
2. more in spring B
3. equal in both
4. nothing can be said

Q. The load versus elongation graph for four wires of the same materials shown in the figure. The thinnest wire is represented by the line:

1. OC
2. OD
3. OA
4. OB

Q. A vessel is filled with an ideal gas at a pressure of $10$ atm and temperature ${27}^{\circ }C$. Half of the mass is removed from the vessel and temperature of the remaining gas is increased to ${87}^{\circ }C$. Then the pressure of the gas in the vessel will be:

1. $7$ atm
2. $5$ atm
3. $6$ atm
4. $8$ atm

Q. In a simple slit diffraction pattern fringes are of:

1. unequal width
2. equal width
3. equal width and equal intensity
4. unequal width and unequal intensity

Q. Consider the radiation emitted by the human body. Which of the following statements is true?

1. The radiation is emitted only during the day.
2. The radiation emitted is in the infrared region.
3. The radiation is emitted during the summers and absorbed during the winters.
4. The radiation emitted lies in the ultraviolet region and hence is not visible.

Q. The radius $R$ of the soap bubble is doubled under iso-thermal condition. If $T$ be the surface tension of soap bubble. The work done in doing so is given by:

1. $24\pi R^{2}T$
2. $8\pi R^{2}T$
3. $32\pi R^{2}T$
4. $4\pi R^{2}T$

Q. A gas is compressed at a constant temperature. Its molecules gain:

1. speed
2. kinetic energy
3. internal energy
4. none of these

Q. A black body at a temperature of ${227}^{\circ }C$ radiates heat energy at the rate $5cal/c{m}^2/s$. At a temperature of ${727}^{\circ }C$, the rate of heat radiated per unit area in $cal/c{m}^2$ will be:

1. $500$
2. $250$
3. $80$
4. $160$

Q. If the body is moving in a circle of radius $r$ with a constant speed $v$. Its angular velocity is:

1. $\frac{v^2}{r}$
2. $vr$
3. $\frac{v}{r}$
4. $\frac{r}{v}$

Q. A ball of mass $0.25$ kg attached to the end of a string of length $1.96$ m is moving in a horizontal circle. The string will break if the tension is more than $25$ N. What is the maximum speed with which ball can be moved?

1. $3$ m/s
2. $3.92$ m/s
3. $5$ m/s
4. $14$ m/s

Q. A car of mass $1500$ kg is moving with a speed of $12.5$ m/s on a circular path of radius $20$ m on a level road. What should be the coefficient of friction between the car and the road, so that the car does not slip?

1. $0.2$
2. $0.6$
3. $0.8$
4. $0.4$

Q. Young's modulus of the material of a wire is Y. If it is under a stress S, the energy stored per unit volume is given by:

1. $\frac{1}{2}\frac{S^2}{Y}$
2. $\frac{1}{2}\frac{S}{Y}$
3. $\frac{1}{2}\frac{S}{Y^2}$
4. $\frac{1}{2}\frac{S^2}{Y^2}$

Q. A particle executes a simple harmonic motion of time period $T$. Find the time taken by the particle to go directly from its mean position to half the amplitude.

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

Q. A glass slab of thickness $4$ cm contains the same numbers of waves as $5$ cm of water when both are traversed by the same monochromatic ray of light. The refractive index of water is $\frac{4}{3}$, what is that for glass?

1. $\frac{5}{3}$
2. $\frac{5}{4}$
3. $\frac{16}{15}$
4. $\frac{3}{2}$

Q. If the temperature increases, then what happens to the frequency of the sound produced by the organ pipe?

1. Increases
2. Decreases
3. Unchanged
4. Not definite

Q. For the stationary wave $Y=4sin\left(\begin{array}{c}\frac{\pi x}{15}\end{array}\right)cos\left(96\pi t\right)$, the distance between a node and the next anti-node is(in cm) :

1. $7.5$
2. $15$
3. $22.5$
4. $30$

Q. A plane wave front of wavelength $\lambda$ is incident on a single slit of width b. What is the angular width for secondary maximum?

1. $\frac{\lambda }{2b}$
2. $\frac{2\lambda }{b}$
3. $\frac{b}{\lambda }$
4. $\frac{\lambda }{b}$

Q. In a resonance tube the first resonance with a tuning fork occurs at $16$ cm and second at $49$ cm. If the velocity of sound is $330$ m/s, the frequency of tuning fork is :

1. $500$
2. $300$
3. $330$
4. $165$

Q. A wheel has a speed of $1200$ revolution per minute and is made to slow down at a rate of $4rad/s^2$. The number of revolution it makes before coming to rest is

1. $314$
2. $722$
3. $143$
4. $272$

Q. Bernoulli's equation is conservation of:

1. Momentum
2. Energy
3. Angular momentum
4. Mass

Q. In the production of beats by two waves of same amplitude and nearly same frequency, the maximum intensity to each of the constituent waves is

1. Same
2. $2$ times
3. $4$ times
4. $8$ times

Q. Two wires A and B are of the same materials. Their lengths are in the ratio $1:2$ and the diameters are in the ratio $2:1$, When stretched by force $F_A$ and $F_B$ respectively they get equal increase in their lengths. Then the ratio $\frac{F_A}{F_B}$ should be:

1. $8:1$
2. $1:2$
3. $1:1$
4. $2:1$

Q. Which of the following is the evidence to show that there must be a force acting on earth and directed towards the sun?

1. Deviation of the falling bodies towards east
2. Revolution of the earth around the sun
3. Phenomenon of day and night
4. Apparent motion of sun round the earth

Q. The mass of earth is $81$ times that of the moon and the radius of the earth is $3.5$ times that of the moon. The ratio of the escape velocity on the surface of earth to that on the surface of moon will be:

1. $0.2$
2. $2.57$
3. $4.81$
4. $0.39$

Q. The tourmaline crystal:

1. absorbs ordinary light and transmits extra ordinary
2. absorbs extra ordinary light and transmits ordinary light
3. absorbs both ordinary and extra ordinary light
4. transmits both ordinary light and extra ordinary light

Q. A sphere is suspended by a thread of length $l$ . What minimum horizontal velocity has to be imparted the ball for it to reach the height of the suspension?

1. $2gl$
2. $gl$
3. $\sqrt{2gl}$
4. $\sqrt{gl}$

Q. A circular disc is to be made by using iron and aluminium, so that it acquires maximum momentum of inertia about its geometrical axis. It is possible with

1. Aluminium at interior and iron surrounding it
2. Iron and aluminium layers in alternate order
3. Either (a) or (c)
4. Iron at interior and aluminium surrounding it