Practice Questions

Q23.Two plates A and B have thermal conductivities 84 W m-1 K-1 and 126 W m-1 K-1 respectively. They have same surface area and same thickness. They are placed in contact along their surfaces. If the temperatures of the outer surfaces of A and B are kept at 100∘C and 0∘C respectively, then the temperature of the surface of contact in steady state is_____ ∘C.

Q23.A solid sphere of mass 1 kg rolls without slipping on a plane surface. Its kinetic energy is 7 × 10-3 J. The speed of the centre of mass of the sphere is ______ cm s-1.

Q23.A solid sphere of mass 500 g radius 5 cm is rotated about one of its diameter with angular speed of 10 rad s-1. If the moment of inertia of the sphere about its tangent is 𝑥× 10-2 times its angular momentum about the diameter. Then the value of 𝑥 will be

Q23.Solid sphere 𝐴 is rotating about an axis 𝑃𝑄. If the radius of the sphere is 5 cm, then its radius of gyration about 𝑃𝑄 will be √𝑥 cm. The value of 𝑥 is _____.

Q23.An oscillating LC circuit consists of a 75 mH inductor and a 1. 2 µF capacitor. If the maximum charge to the capacitor is 2. 7 µC. The maximum current in the circuit will be _______ mA.

Q23.There is an air bubble of radius 1. 0 mm in a liquid of surface tension 0. 075 N m–1 and density 1000 kg m–3 at a depth of 10 cm below the free surface. The amount by which the pressure inside the bubble is greater than the atmospheric pressure is _______ Pa(g = 10 m s−2).

Q23.A certain pressure '𝑃' is applied to 1 litre of water and 2 litre of a liquid separately. Water gets compressed to 0 . 01% whereas the liquid gets compressed to 0 . 03%. The ratio of Bulk modulus of water to that of the liquid 3 is 𝑥. The value of 𝑥 is ______.

Q24.A series LCR circuit is connected to an AC source of 220 V , 50 Hz. The circuit contains a resistance R = 80 Ω, an inductor of inductive reactance XL = 70 Ω, and a capacitor of capacitive reactance XC = 130 Ω . The power factor of circuit is x . The value of x is: 10

Q24.The fundamental frequency of vibration of a string between two rigid support is 50 Hz. The mass of the string is 18 g and its linear mass density is 20 g m−1 . The speed of the transverse waves so produced in the string is _______ m s–1 .

Q24.A fish rising vertically upward with a uniform velocity of 8 m s–1, observes that a bird is diving vertically downward towards the fish with the velocity of 12 m s–1. If the refractive index of water is 34 , then the actual velocity of the diving bird to pick the fish, will be __________m s−1.

Q24.As shown in figures, three identical polaroids P1 , P2 and P3 are placed one after another. The pass axis of P2 and P3 are inclined at angle of 60º and 90º with respect to axis of P1 . The source S has an intensity of 256 W m−2 . The intensity of light at point O is _____ W m−2 . ∘

Q24.Two transparent media having refractive indices 1. 0 and 1. 5 are separated by a spherical refracting surface of radius of curvature 30 cm. The centre of curvature of surface is towards denser medium and a point object is placed on the principal axis in rarer medium at a distance of 15 cm from the pole of the surface. The distance of image from the pole of the surface is cm.

Q24.A rectangular block of mass 5 kg attached to a horizontal spiral spring executes simple harmonic motion of amplitude 1 m and time period 3 . 14 s. The maximum force exerted by spring on block is ___ N.

Q24.A thin rod having a length of 1 m and area of cross-section 3 × 10-6 m2 is suspended vertically from one end. The rod is cooled from 210°C to 160°C. After cooling, a mass 𝑀 is attached at the lower end of the rod such that the length of rod again becomes 1 m. Young's modulus and coefficient of linear expansion of the rod are 2 × 1011 N m-2 and 2 × 10-5 K-1, respectively. The value of 𝑀 is ______ kg. (Take 𝑔= 10 m s-2 )

Q24.The amplitude of a particle executing SHM is 3 cm. The displacement at which its kinetic energy will be 25% more than the potential energy is: ______ cm.

Q24.A capacitor of capacitance 900 µ F is charged by a 100 V battery. The capacitor is disconnected from the battery and connected to another uncharged identical capacitor such that one plate of uncharged capacitor connected to positive plate and another plate of uncharged capacitor connected to negative plate of the charged capacitor. The loss of energy in this process is measured as 𝑥× 10-2 J. The value of 𝑥 is ______.

Q24.In a Young’s double slit experiment, the intensities at two points, for the path difference λ and λ ( λ being the 4 3 wavelength of light used) are I1 and I2 respectively. If I0 denotes the intensity produced by each one of the individual slits, then I1+I2 = ______ . I0

Q24.A ray of light is incident from air on a glass plate having thickness √3 cm and refractive index √2 . The angle of incidence of a ray is equal to the critical angle for glass-air interface. The lateral displacement of the ray when it passes through the plate is ____ × 10−2 cm . (given sin 15°= 0. 26 )

Q24.In an experiment with sonometer when a mass of 180 g is attached to the string, it vibrates with fundamental frequency of 30 Hz. When a mass 𝑚 is attached, the string vibrates with fundamental frequency of 50 Hz. The value of 𝑚 is ______ g.

Q24.The length of a wire becomes 𝑙1 and 𝑙2 when 100 N and 120 N tension are applied respectively. If 1 10𝑙2 = 11𝑙1, then the natural length of wire will be 𝑥𝑙1. Here the value of 𝑥 is 𝜋

Q25.A convex lens of refractive index 1. 5 and focal length 18 cm in air is immersed in water. The change in focal length of the lens will be_____ cm. (Given refractive index of water = 43 )

Q25.In the given figure the total charge stored in the combination of capacitors is 100 µC. The value of ‘ x’ is ______________.

Q25.Three concentric spherical metallic shells 𝑋, 𝑌 and 𝑍 of radius 𝑎, 𝑏 and 𝑐 respectively 𝑎< 𝑏< 𝑐 have surface charge densities 𝜎, – 𝜎 and 𝜎, respectively. The shells 𝑋 and 𝑍 are at same potential. If the radii of 𝑋 & 𝑌 are 2 cm and 3 cm, respectively. The radius of shell 𝑍 is _____cm. Q26.10 resistors each of resistance 10 Ω can be connected in such as to get maximum and minimum equivalent resistance. The ratio of maximum and minimum equivalent resistance will be________.

Q25.Unpolarised light is incident on the boundary between two dielectric media, whose dielectric constants are 2. 8 (medium – 1) and 6. 8 (medium – 2), respectively. To satisfy the condition, so that the reflected and refracted 1 rays are perpendicular to each other, the angle of incidence should be tan−1 (1 + 10θ ) 2 , the value of θ is ______. (Given for dielectric media, μr = 1 )

Q25.Two vertical parallel mirrors A and B are separated by 10 cm. A point object O is placed at a distance of 2 cm from mirror A. The distance of the second nearest image behind mirror A from the mirror A is _______ cm.