Q. A particle performing S.H.M. starts from equilibrium position and its time period is $16$ second. After $2$ seconds its velocity is $\pi m/s$. Amplitude of oscillation is $(\cos {45}^{\circ }=\frac{1}{\sqrt{2}})$

1. $2\sqrt{2}m$
2. $4\sqrt{2}m$
3. $6\sqrt{2}m$
4. $8\sqrt{2}m$

Q. A particle performs linear S.H.M. At a particular instant, velocity of the particle is ${}^{\prime }{u}^{\prime }$ and acceleration is ${}^{\prime }{\alpha }^{\prime }$ while at another instant velocity is ${}^{\prime }{v}^{\prime }$ and acceleration is ${}^{\prime }{\beta }^{\prime }(0<\alpha <\beta )$. The distance between the two positions is

1. $\frac{u^2+v^2}{\alpha +\beta }$
2. $\frac{u^2-v^2}{\alpha +\beta }$
3. $\frac{u^2-v^2}{\alpha -\beta }$
4. $\frac{u^2+v^2}{\alpha -\beta }$

Q. A metal rod of length ${}^{\prime }{L}^{\prime }$ and cross-sectional area ${}^{\prime }{A}^{\prime }$ is heated through ${}^{\prime }{T}^{\prime \circ }C$. What is the force required to prevent the expansion of the rod lengthwise?
$[Y=$ Young's modulus of the material of rod, $\alpha -$ coefficient of linear expansion]

1. $\frac{YA\alpha T}{(1-\alpha T)}$
2. $\frac{YA\alpha T}{(1+\alpha T)}$
3. $\frac{(1-\alpha T)}{YA\alpha T}$
4. $\frac{(1+\alpha T)}{YA\alpha T}$

Q. A flywheel at rest is to reach an angular velocity of $24rad/s$ in $8$ second with constant angular acceleration. The total angle turned through during this interval is

1. $96rad$
2. $48rad$
3. $24rad$
4. $72rad$

Q. The frequencies for series limit of Balmer and Paschen series respectively are ${}^{\prime }{v}_1^{\prime }$ and ${}^{\prime }{v}_3^{\prime }$. If frequency of first line of Balmer series is ${}^{\prime }{v}_2^{\prime }$ then the relation between ${}^{\prime }{v}_1^{\prime }{,}^{\prime }{v}_2^{\prime }$ and ${}^{\prime }{v}_3^{\prime }$ is

1. $v_1-v_2=v_3$
2. $v_1+v_3=v_2$
3. $v_1+v_2=v_3$
4. $v_1-v_3=2v_1$

Q. A big water drop is formed by the combination of ${}^{\prime }{n}^{\prime }$ small water drops of equal radii. The ratio of the surface energy of ${}^{\prime }{n}^{\prime }$ drops to the surface energy of big drop is

1. $n^2:1$
2. $n:1$
3. $\sqrt[3]{3n}:1$
4. $\sqrt{n}:1$

Q. The depth ${}^{\prime }{d}^{\prime }$ at which the value of acceleration due to gravity becomes $\frac{1}{n}$ times the value at the earth's surface is $(R=$ radius of earth)

1. $d=R\left(\frac{n}{n-1}\right)$
2. $d=R\left(\frac{n-1}{n}\right)$
3. $d=R\left(\frac{n-1}{2n}\right)$
4. $d=R^2\left(\frac{n-1}{n}\right)$

Q. For a particle moving in vertical circle, the total energy at different positions along the path

1. is conserved
2. increases
3. decreases
4. may increase or decrease

Q. Two spherical black bodies have radii ${}^{\prime }{r}_1^{\prime }$ and ${}^{\prime }{r}_2^{\prime }$. Their surface temperatures are ${}^{\prime }{T}_1^{\prime }$ and ${}^{\prime }{T}_2^{\prime }$. If they radiate same power then $\frac{r_2}{r_1}$ is

1. $\frac{T_1}{T_2}$
2. ${\left(\frac{T_1}{T_2}\right)}^2$
3. ${\left(\frac{T_2}{T_1}\right)}^2$
4. $\frac{T_2}{T_1}$

Q. A solid sphere of mass $2kg$ is rolling on a frictionless horizontal surface with velocity $6m/s$. It collides on the free end of an ideal spring whose other end is fixed. The maximum compression produced in the spring will be (Force constant of the spring $=36N/m)$

1. $\sqrt{14}m$
2. $\sqrt{2.8}m$
3. $\sqrt{1.4}m$
4. $\sqrt{0.7}m$

Q. A disc of moment of inertia ${}^{\prime }{I}_1^{\prime }$ is rotating in horizontal plane about an axis passing through a centre and perpendicular to its plane with constant angular speed ${}^{\prime }{\omega }_1^{\prime }$. Another disc of moment of inertia ${}^{\prime }{I}_2^{\prime }$ having zero angular speed is placed coaxially on a rotating disc. Now both the discs are rotating with constant angular speed ${}^{\prime }{\omega }_2^{\prime }$. The energy lost by the initial rotating disc is

1. $\frac{1}{2}\left[\frac{I_1{I}_2}{I_1-I_2}\right]{\omega }_1^2$
2. $\frac{1}{2}\left[\frac{I_1+I_2}{I_1{I}_2}\right]{\omega }_1^2$
3. $\frac{1}{2}\left[\frac{I_1-I_2}{I_1{I}_2}\right]{\omega }_1^2$
4. $\frac{1}{2}\left[\frac{I_1{I}_2}{I_1+I_2}\right]{\omega }_1^2$

Q. Two uniform wires of the same material are vibrating under the same tension. If the first overtone of the first wire is equal to the second overtone of the second wire and radius of the first wire is twice the radius of the second wire then the ratio of the lengths of the first wire to second wire is

1. $\frac{1}{3}$
2. $\frac{1}{5}$
3. $\frac{1}{4}$
4. $\frac{1}{6}$

Q. Sensitivity of moving coil galvanometer is '$s$'. If a shunt of ${\left(\frac{1}{8}\right)}^{th}$ of the resistance of galvanometer is connected to moving coil galvanometer, its sensitivity becomes:

1. $\frac{s}{3}$
2. $\frac{s}{6}$
3. $\frac{s}{12}$
4. $\frac{s}{9}$

Q. The ratio of binding energy of a satellite at rest on earth's surface to the binding energy of a satellite of same mass revolving around the earth at a height ${}^{\prime }{h}^{\prime }$ above the earth's surface is ($R=$ radius of the earth)

1. $\frac{2(R+h)}{R}$
2. $\frac{R+h}{2R}$
3. $\frac{R+h}{R}$
4. $\frac{R}{R+h}$

Q. The equation of the progressive wave is $Y=3\sin [\pi (\frac{t}{3}-\frac{x}{5})+\frac{\pi }{4}]$ where $x$ and $Y$ are in metre and time in second. Which of the following is correct?

1. Velocity $V=1.5m/s$
2. Frequency $F=0.2Hz$
3. Wavelength $\lambda =10m$
4. Amplitude $A=3cm$

Q. An ideal gas has pressure ${}^{\prime }{P}^{\prime }$, volume ${}^{\prime }{V}^{\prime }$ and absolute temperature ${}^{\prime }{T}^{\prime }$. If ${}^{\prime }{m}^{\prime }$ is the mass of each molecule and ${}^{\prime }{K}^{\prime }$ is the Boltzmann constant then density of the gas is

1. $\frac{Pm}{KT}$
2. $\frac{KT}{Pm}$
3. $\frac{Km}{PT}$
4. $\frac{PK}{Tm}$

Q. A simple pendulum of lenght ${}^{\prime }{L}^{\prime }$ has mass ${}^{\prime }{M}^{\prime }$ and it oscillates freely with amplitude ${}^{\prime }{A}^{\prime }$. At extreme position, its potential energy is
($g=$ acceleration due to gravity)

1. $\frac{Mg{A}^2}{2L}$
2. $\frac{MgA}{2L}$
3. $\frac{Mg{A}^2}{L}$
4. $\frac{2Mg{A}^2}{L}$

Q. When three capacitors of equal capacities are connected in parallel and one of the same capacity is connected in series with its combination. The resultant capacity is $3.75\mu F$. The capacity of each capacitor is

1. $5\mu F$
2. $7\mu F$
3. $6\mu F$
4. $8\mu F$

Q. The closed and open organ pipes have same length. When they are vibrating simultaneously in first overtone, produce three beats. The length of open pipe is made ${\frac{1}{3}}^{rd}$ and close pipe is made three times the original, the number of beats produced will be

1. $8$
2. $14$
3. $20$
4. $17$

Q. A particle is performing S.H.M. starting from extreme position. Graphical representation shows that, between displacement and acceleration, there is a phase difference of

1. $0rad$
2. $\frac{\pi }{4}rad$
3. $\frac{\pi }{2}rad$
4. $\pi rad$

Q. In Fraunhofer diffraction pattern, slit width is $0.2mm$ and screen is at $2m$ away from the lens. If wavelength of light used in $5000\stackrel{\circ }{A}$ then the distance between the first minimum on either side of the central maximum is $(\theta$ is small and measure in radian):

1. ${10}^{-2}m$
2. ${10}^{-1}m$
3. $2\times {10}^{-2}m$
4. $2\times {10}^{-1}m$

Q. When one end of the capillary is dipped in water, the height of water column is ${}^{\prime }{h}^{\prime }$. The upward force of $105$ dyne due to surface tension balanced by the force due to the weight of water column. The inner circumference of the capillary is
(Surface tension of water $=7\times {10}^{-2}N/m)$

1. $1.5cm$
2. $2cm$
3. $2.5cm$
4. $3cm$

Q. A ceiling fan rotates about its own axis with some angular velocity. When the fan is switched off, the angular velocity becomes ${\left(\frac{1}{4}\right)}^{th}$ of the original in time ${}^{\prime }{t}^{\prime }$ and ${}^{\prime }{n}^{\prime }$ revolutions are made in that time. The number of revolutions made by the fan during the time interval between switch off and rest are (Angular retardation is uniform).

1. $\frac{8n}{15}$
2. $\frac{4n}{15}$
3. $\frac{16n}{15}$
4. $\frac{32n}{15}$

Q. A lift of mass ${}^{\prime }{m}^{\prime }$ is connected to a rope which is moving upward with the maximum acceleration ${}^{\prime }{a}^{\prime }$. For maximum safe stress, the elastic limit of the rope is ${}^{\prime }{T}^{\prime }$. The minimum diameter of the rope is $(g=$ gravitational acceleration):

1. ${\left[\frac{2m(g+a)}{\pi T}\right]}^{\frac{1}{2}}$
2. $2{\left[\frac{m(g+a)}{\pi T}\right]}^{\frac{1}{2}}$
3. ${\left[\frac{m(g+a)}{2\pi T}\right]}^{\frac{1}{2}}$
4. ${\left[\frac{m(g+a)}{\pi T}\right]}^{\frac{1}{2}}$

Q. A wheel of moment of inertia $2Kg{m}^2$ is rotating about an axis passing through centre and perpendicular to its plane at a speed $60rad/s$. Due to friction, it comes to rest in $5$ minutes. The angular momentum of the wheel three minutes before it stops rotating is

1. $24Kg{m}^2/s$
2. $48Kg{m}^2/s$
3. $72Kg{m}^2/s$
4. $96Kg{m}^2/s$

Q. Two unknown resistances are connected in two gaps of a meter-bridge. The null point is obtained at $40cm$ from left end. A $30\Omega$ resistance is connected in series with the smaller of the two resistances, the null point shifts by $20cm$ to the right end. The value of smaller resistance in $\Omega$ is

1. $12$
2. $24$
3. $48$
4. $36$

Q. The fundamental frequency of an air column in a pipe closed at one end is $100Hz$. If the same pipe is open at both the ends, the frequencies produced in $Hz$ are

1. $100,200,300,400,.....$
2. $100,300,500,700,....$
3. $200,300,400,500,.....$
4. $200,400,600,800,.....$

Q. For a rigid diatomic molecule, universal gas constant $R=nCp$ where ${}^{\prime }C{p}^{\prime }$ is the molar specific heat at constant pressure and ${}^{\prime }{n}^{\prime }$ is a number. Hence $n$ is equal to

1. $0.4$
2. $0.2857$
3. $0.2257$
4. $0.3557$

Q. In a sonometer experiment, the string of length ${}^{\prime }{L}^{\prime }$ under tension vibrates in second overtone between two bridges. The amplitudes of vibration is maximum at

1. $\frac{L}{6},\frac{L}{2},\frac{5L}{6}$
2. $\frac{L}{8},\frac{L}{4},\frac{L}{2}$
3. $\frac{L}{2},\frac{L}{4},\frac{L}{6}$
4. $\frac{L}{6},\frac{L}{2},\frac{L}{6}$

Q. The observer is moving with velocity ${}^{\prime }{v}_0^{\prime }$ towards the stationary source of sound and then after crossing moves away from the source with velocity ${}^{\prime }{v}_0^{\prime }$. Assume that the medium through which the sound waves travel is at rest. If ${}^{\prime }{v}^{\prime }$ is the velocity of sound and ${}^{\prime }{n}^{\prime }$ is thee frequency emitted by the source then the difference between apparent frequencies heard by the observer is

1. $\frac{2n{v}_0}{v}$
2. $\frac{v}{2n{v}_0}$
3. $\frac{v}{n{v}_0}$
4. $\frac{n{v}_0}{v}$