In the adjacent figure, ABCD are four points in a smooth horizontal plane representing the four corners of a square of diagonal 20 cm . A very small object of mass 144 gm placed at the centre of the s

Question

In the adjacent figure, ABCD are four points in a smooth horizontal plane representing the four corners of a square of diagonal 20 cm . A very small object of mass 144 gm placed at the centre of the square connected to points $A, B, C$ and D by four elastic strings of same dimensions but of different moduli of elasticity as shown in the figure. Natural length and cross-sectional area of each string are 10 cm and $1 0^{- 6} m^{2}$ respectively. The mass is slightly displaced from equilibrium and then released to perform SHM along the diagonal AC. $(Y_{1} = 9 Y, Y_{2} = 4 Y, Y_{3} = 16 Y$ and $Y_{4} = 4 Y$ , where $Y = 4.9 \times 1 0^{9} N / m^{2})$ . The time period of oscillation of object is K millisecond. The value of K is approximately

TestHub · Accepted Answer

T = π [ 9 YA m ℓ ​ ​ + 16 YA m ℓ ​ ​ ] = π [ YA m ℓ ​ ​ ] [ 3 1 ​ + 4 1 ​ ] = 12 7 π ​ YA m ℓ ​ ​ m = 144 × 1 0 − 3 kg ℓ = AO = BO = CO = DO = 10 × 1 0 − 2 m ​ A = π 2 × 1 0 − 6 m 2 Y = 4.9 × 1 0 9 ​ ​ T = 12 7 π ​ π 2 × 1 0 − 6 × 49 × 1 0 8 144 × 1 0 − 3 × 10 × 1 0 − 2 ​ ​ = 12 7 π ​ × π 12 ​ × 7 1 ​ 1 0 8 1 0 − 2 ​ ​ = 1 × 1 0 − 3 = 1 ms

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