Practice Questions

Q23.A plane is in level flight at constant speed and each of its two wings has an area of 40 m2 . If the speed of the air is 180 km h-1 over the lower wing surface and 252 km h-1 over the upper wing surface, the mass of the plane is ________kg . (Take air density to be 1 kg m – 3 and 𝑔= 10 m s – 2)

Q23.Two blocks of mass 2 kg and 4 kg are connected by a metal wire going over a smooth pulley as shown in figure. The radius of wire is 4 . 0 × 10-5 m and Young's modulus of the metal is 2 . 0 × 1011 N m-2. The 𝛼 is _____. [Use 𝑔= 10 m s-2) longitudinal strain developed in the wire is 𝛼𝜋.1 The value of 𝛼 is

Q23.A wire of cross sectional area A, modulus of elasticity 2 × 1011Nm−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 JEE Main 2024 (06 Apr Shift 2) JEE Main Previous Year Paper making angle θ = 1001 radian on the points of support. The value of A is _______ ×10−4 m2 (consider x << L ). (given : g = 10 m/s2 )

Q23.Each of three blocks P, Q and R shown in figure has a mass of 3 kg. Each of the wire A and B has cross- sectional area 0. 005 cm2 and Young's modulus 2 × 1011 N m−2 . Neglecting friction, the longitudinal strain on wire B is _____ ×10−4 . (Take g = 10 m s−2 ) JEE Main 2024 (30 Jan Shift 1) JEE Main Previous Year Paper

Q23.A circular disc reaches from top to bottom of an inclined plane of length l. When it slips down the plane, if α is _________ takes t s. When it rolls down the plane then it takes ( α2 )1/2t s, where

Q23.An elastic spring under tension of 3 N has a length a . Its length is b under tension 2 N . For its length (3a −2b) , the value of tension will be______ N .

Q23.In a test experiment on a model aeroplane in wind tunnel, the flow speeds on the upper and lower surfaces of the wings are 70 m s−1 and 65 m s−1 respectively. If the wing area is 2 m2 , the lift of the wing is _______ N . (Given density of air = 1. 2 kg m−3 )

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 × 1011 N m−2 . Original length of the wire is 2 m and the area of cross section is 2 cm2 . The wire will extend in length by ______ μm .

Q23.A big drop is formed by coalescing 1000 small identical drops of water. If 𝐸1 be the total surface energy of 1000 small drops of water and 𝐸2 be the surface energy of single big drop of water, the 𝐸1 : 𝐸2 is 𝑥: 1, where 𝑥= ________.

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 10 . The value of x is __________ x

Q23.If average depth of an ocean is 4000 m and the bulk modulus of water is 2 × 109 N m−2 , then fractional compression ΔV of water at the bottom of ocean is α × 10−2 . The value of α is _______, (Given, V g = 10 m s−2, ρ = 1000 kg m−3 )

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

Q23.One end of a metal wire is fixed to a ceiling and a load of 2 kg hangs from the other end. A similar wire is attached to the bottom of the load and another load of 1 kg hangs from this lower wire. Then the ratio of longitudinal strain of upper wire to that of the lower wire will be [Area of cross section of wire = 0 . 005 cm2, 𝑌= 2 × 1011 N m-2 and 𝑔= 10 m s-2]

Q23.Two metallic wires P and Q have same volume and are made up of same material. If their area of cross sections are in the ratio 4 : 1 and force F1 is applied to P , an extension of Δl is produced. The force which is required to produce same extension in Q is F2 . The value of F1F2 is ______.

Q23. A hydraulic press containing water has two arms with diameters as mentioned in the figure. A force of 10 N is applied on the surface of water in the thinner arm. The force required to be applied on the surface of water in the thicker arm to maintain equilibrium of water is _____N.

Q24.A tuning fork resonates with a sonometer wire of length 1 m stretched with a tension of 6 N . When the tension in the wire is changed to 54 N, the same tuning fork produces 12 beats per second with it. The frequency of the tuning fork is _______ Hz .

Q24.Two open organ pipes of lengths 60 cm and 90 cm resonate at 6th and 5th harmonics respectively. The difference of frequencies for the given modes is _______ Hz . (Velocity of sound in air = 333 m/s )

Q24.A particle performs simple harmonic motion with amplitude 𝐴. Its speed is increased to three times at an 2𝐴 𝑛𝐴 instant when its displacement is . The new amplitude of motion is . The value of 𝑛 is _____. 3 3

Q24.A closed organ pipe 150 cm long gives 7 beats per second with an open organ pipe of length 350 cm, both vibrating in fundamental mode. The velocity of sound is ______ m s-1.

Q24.A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is ( a−1a ) then the value of a is ________ → 2^i+6^j+8^k 2^i+^j+^k . The

Q24.The time period of simple harmonic motion of mass 𝑀 in the given figure is 𝜋√ 𝛼𝑀5𝐾, where the value of _______. JEE Main 2024 (31 Jan Shift 2) JEE Main Previous Year Paper

Q24.The displacement of a particle executing SHM is given by x = 10 sin (wt + π3 )m. The time period of motion is 3.14 s. The velocity of the particle at t = 0 is ______ m/s.

Q24.In a closed organ pipe, the frequency of fundamental note is 30 Hz. A certain amount of water is now poured in the organ pipe so that the fundamental frequency is increased to 110 Hz. If the organ pipe has a cross- sectional area of 2 cm2 , the amount of water poured in the organ tube is ________ g. (Take speed of sound in air is 330 m s−1 )

Q24.The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes of 4 m, 2 ms−1 and 16 ms−2 at a certain instant. The amplitude of the motion is √x, m where x is ________

Q24.At room temperature (27∘C), the resistance of a heating element is 50Ω. The temperature coefficient of the material is 2.4 × 10−4∘C−1 . The temperature of the element, when its resistance is 62Ω, is _____ ∘C.