Practice Questions

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 × 103 kg m−3 and surface tension of soap solution is 0.28Nm−1 , then diameter of the soap bubble is _____ cm . (if 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.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.The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by 0 . 02% is _____ m. (Take density of sea water = 103 kg m-3, Bulk modulus of rubber = 9 × 108 N m-2, and 𝑔= 10 m s-2)

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.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. 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.

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.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 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.The density and breaking stress of a wire are 6 × 104 kg/m3 and 1.2 × 108 N/m2 respectively. The wire is 1 rd suspended from a rigid support on a planet where acceleration due to gravity is of the value on the surface 3 of earth. The maximum length of the wire with breaking is _____ m (take, g = 10 m/s2 ).

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.The reading of pressure metre attached with a closed pipe is 4 . 5 × 104 N m-2. On opening the valve, water starts flowing and the reading of pressure metre falls to 2 . 0 × 104 N m-2. The velocity of water is found to be √𝑉 m s-1. The value of 𝑉 is _________.

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.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 = 105Nm−2 , density of mercury = 1.36 × 104 kg m− 3, g = 10 m s−2, π = 227 )

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.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]

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.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 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 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.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.A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is 4 m, then the time period of small oscillations will be _________s. [take 𝑔= 𝜋2 m s-2]

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.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