Q22. If the radius of earth is reduced to three-fourth of its present value without change in its mass then value of duration of the day of earth will be $\_\_\_\_$ hours 30 minutes.

Q22. Three balls of masses $2 \mathrm {~kg} , 4 \mathrm {~kg}$ and 6 kg respectively are arranged at centre of the edges of an equilateral triangle of side 2 m . The moment of intertia of the system about an axis through the centroid and perpendicular to the plane of triangle, will be $\_\_\_\_$ $\mathrm { kgm } ^ { 2 }$.

Q22. A uniform thin metal plate of mass 10 kg with dimensions is shown. The ratio of x and y coordinates of center [Figure] of mass of plate in $\frac { n } { 9 }$. The value of $n$ is $\_\_\_\_$

Q22. A circular table is rotating with an angular velocity of $\omega \mathrm { rad } / \mathrm { s }$ about its axis (see figure). There is a smooth groove along a radial direction on the table. A steel ball is gently placed at a distance of 1 m on the groove. All the surfaces are smooth. If the radius of the table is 3 m , the radial velocity of the ball w.r.t. the table at the [Figure] time ball leaves the table is $x \sqrt { 2 } \omega \mathrm {~m} / \mathrm { s }$, where the value of $x$ is $\_\_\_\_$ .

Q23. An elastic spring under tension of 3 N has a length $a$. Its length is $b$ under tension 2 N . For its length $( 3 a - 2 b )$ , the value of tension will be $\_\_\_\_$ N.

Q23. Mercury is filled in a tube of radius 2 cm up to a height of 30 cm . The force exerted by mercury on the bottom of the tube is $\_\_\_\_$ N . (Given, atmospheric pressure $= 10 ^ { 5 } \mathrm { Nm } ^ { - 2 }$, density of mercury $= 1.36 \times 10 ^ { 4 } \mathrm {~kg} \mathrm {~m} ^ { - } { } ^ { 3 } , \mathrm {~g} = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 } , \pi = \frac { 22 } { 7 }$ )

Q23. The density and breaking stress of a wire are $6 \times 10 ^ { 4 } \mathrm {~kg} / \mathrm { m } ^ { 3 }$ and $1.2 \times 10 ^ { 8 } \mathrm {~N} / \mathrm { m } ^ { 2 }$ respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is $\frac { 1 } { 3 } ^ { \text {rd } }$ of the value on the surface of earth. The maximum length of the wire with breaking is $\_\_\_\_$ m (take, $\mathrm { g } = 10 \mathrm {~m} / \mathrm { s } ^ { 2 }$ ).

Q23. A big drop is formed by coalescing 1000 small droplets of water. The ratio of surface energy of 1000 droplets to that of energy of big drop is $\frac { 10 } { x }$. The value of $x$ is $\_\_\_\_$

Q23. A wire of cross sectional area A, modulus of elasticity $2 \times 10 ^ { 11 } \mathrm { Nm } ^ { - 2 }$ and length 2 m is stretched between two vertical rigid supports. When a mass of 2 kg is suspended at the middle it sags lower from its original position making angle $\theta = \frac { 1 } { 100 }$ radian on the points of support. The value of $A$ is $\_\_\_\_$ $\times 10 ^ { - 4 } \mathrm {~m} ^ { 2 }$ (consider [Figure] $x \ll \mathrm {~L}$ ). (given : $\mathrm { g } = 10 \mathrm {~m} / \mathrm { s } ^ { 2 }$ )

Q23. A liquid column of height 0.04 cm balances excess pressure of a soap bubble of certain radius. If density of liquid is $8 \times 10 ^ { 3 } \mathrm {~kg} \mathrm {~m} ^ { - 3 }$ and surface tension of soap solution is $0.28 \mathrm { Nm } ^ { - 1 }$, then diameter of the soap bubble is $\_\_\_\_$ cm . (if $g = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ )

Q23. Small water droplets of radius 0.01 mm are formed in the upper atmosphere and falling with a terminal velocity of $10 \mathrm {~cm} / \mathrm { s }$. Due to condensation, if 8 such droplets are coalesced and formed a larger drop, the new terminal velocity will be $\_\_\_\_$ $\mathrm { cm } / \mathrm { s }$.

Q23. Two persons pull a wire towards themselves. Each person exerts a force of 200 N on the wire. Young's modulus of the material of wire is $1 \times 10 ^ { 11 } \mathrm {~N} \mathrm {~m} ^ { - 2 }$. Original length of the wire is 2 m and the area of cross section is $2 \mathrm {~cm} ^ { 2 }$. The wire will extend in length by $\_\_\_\_$ $\mu \mathrm { m }$.

Q24. A soap bubble is blown to a diameter of 7 cm .36960 erg of work is done in blowing it further. If surface tension of soap solution is 40 dyne $/ \mathrm { cm }$ then the new radius is $\_\_\_\_$ cm Take $\left( \pi = \frac { 22 } { 7 } \right)$

Q24. Three capacitors of capacitances $25 \mu \mathrm {~F} , 30 \mu \mathrm {~F}$ and $45 \mu \mathrm {~F}$ are connected in parallel to a supply of 100 V . Energy stored in the above combination is E. When these capacitors are connected in series to the same supply, the stored energy is $\frac { 9 } { x } \mathrm { E }$. The value of $x$ is $\_\_\_\_$ .

Q24. A sonometer wire of resonating length 90 cm has a fundamental frequency of 400 Hz when kept under some tension. The resonating length of the wire with fundamental frequency of 600 Hz under same tension $\_\_\_\_$ cm

Q24. A particle is doing simple harmonic motion of amplitude 0.06 m and time period 3.14 s . The maximum velocity of the particle is $\_\_\_\_$ $\mathrm { cm } / \mathrm { s }$.

Q24. Two open organ pipes of lengths 60 cm and 90 cm resonate at $6 ^ { \text {th } }$ and $5 ^ { \text {th } }$ harmonics respectively. The difference of frequencies for the given modes is $\_\_\_\_$ Hz. (Velocity of sound in air $= 333 \mathrm {~m} / \mathrm { s }$ )

Q24. A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is $\left( \frac { a - 1 } { a } \right)$ then the value of a is $\_\_\_\_$

Q24. An object of mass 0.2 kg executes simple harmonic motion along x axis with frequency of $\left( \frac { 25 } { \pi } \right) \mathrm { Hz }$. At the position $x = 0.04 \mathrm {~m}$ the object has kinetic energy 0.5 J and potential energy 0.4 J . The amplitude of oscillation is $\_\_\_\_$ cm .

Q24. The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes of $4 \mathrm {~m} , 2 \mathrm {~ms} ^ { - 1 }$ and $16 \mathrm {~ms} ^ { - 2 }$ at a certain instant. The amplitude of the motion is $\sqrt { x } , \mathrm {~m}$ where $x$ is

Q24. At room temperature ( $27 ^ { \circ } \mathrm { C }$ ), the resistance of a heating element is $50 \Omega$. The temperature coefficient of the material is $2.4 \times 10 ^ { - 4 } { } ^ { \circ } \mathbf { C } ^ { - 1 }$. The temperature of the element, when its resistance is $62 \Omega$, is $\_\_\_\_$ ${ } ^ { \circ } \mathrm { C }$.

Q25. An infinite plane sheet of charge having uniform surface charge density $+ \sigma _ { s } \mathrm { C } / \mathrm { m } ^ { 2 }$ is placed on $x - y$ plane. Another infinitely long line charge having uniform linear charge density $+ \lambda _ { e } \mathrm { C } / \mathrm { m }$ is placed at $z = 4 \mathrm {~m}$ plane and parallel to $y$-axis. If the magnitude values $\left| \sigma _ { \mathrm { s } } \right| = 2 \left| \lambda _ { \mathrm { e } } \right|$ then at point ( $0,0,2$ ), the ratio of magnitudes of electric field values due to sheet charge to that of line charge is $\pi \sqrt { n } : 1$. The value of $n$ is $\_\_\_\_$ .

Q25. A parallel plate capacitor of capacitance 12.5 pF is charged by a battery connected between its plates to potential difference of 12.0 V . The battery is now disconnected and a dielectric slab ( $\epsilon _ { \mathrm { r } } = 6$ ) is inserted between the plates. The change in its potential energy after inserting the dielectric slab is $\_\_\_\_$ $10 ^ { - 12 } \mathrm {~J}$.

Q25. The electric field between the two parallel plates of a capacitor of $1.5 \mu \mathrm {~F}$ capacitance drops to one third of its initial value in $6.6 \mu \mathrm {~s}$ when the plates are connected by a thin wire. The resistance of this wire is $\_\_\_\_$ $\Omega$. (Given, $\log 3 = 1.1$ )

Q25. The electric field at point $p$ due to an electric dipole is $E$. The electric field at point $R$ on equitorial line will be [Figure]