A heavy ball of mass M is suspended from the ceiling of a car by a light string of mass m m ≪ M . When the car is at rest, the speed of transverse waves in the string is 60 ms - 1 . When the car has acceleration a , the wave-speed increases to 60.5 ms - 1 . The value of a , in terms of gravitational acceleration g , is closed to

Question

A heavy ball of mass M is suspended from the ceiling of a car by a light string of mass m m ≪ M . When the car is at rest, the speed of transverse waves in the string is 60 ms - 1 . When the car has acceleration a , the wave-speed increases to 60.5 ms - 1 . The value of a , in terms of gravitational acceleration g , is closed to, g 10, g 20, g 5, g 30

MARKS App · Accepted Answer

For standing car, v = T μ = M g μ For accelerating car, υ ′ = ( M g ) 2 + ( M a ) 2 μ ⇒ 60.5 60 = ( M g ) 2 + ( M a ) 2 M g ⇒ 1 + 1 120 2 = ( M g ) 2 + ( M a ) 2 M g ⇒ 1 + 2 120 = 1 + a 2 g 2 ≈ 2 120 = 1 2 a 2 g 2 ∴ a = g 4 120 = g 30 ≈ g 5

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