A spring balance has a scale that reads from 0 to 50 kg. The length of the scale is 20 cm. A body suspended from this balance, when displaced and released, oscillates with a period of 0.6 s. What is the weight of the body ?
Given: The scale of spring balance reads from 0 to 50 kg , the length of the scale is 20 cm and the period of oscillation of spring balance is 0.6 s .
The maximum force exerted on the spring is given as,
F = M g
Where, the maximum mass that the scale can read is M , acceleration due to gravity is g .
By substituting the given values in above equation, we get
F = 50 × 9.8 = 490 N
The spring force of the balance is given as,
F = k x
Where, the spring force is F , the spring constant is k and the displacement is x .
By substituting the given values in above equation, we get
490 = k × 0.2 k = 490 0.2 = 2450 N / m
The time period of oscillation is given as,
T = 2 π m k
Where, the time period of oscillation is T and the mass of spring balance is m .
By substituting the given values in above equation, we get
0.6 = 2 π m 2450 m 2450 = 0.6 2 π m 2450 = ( 0.6 2 π ) 2 m = 2450 × ( 0.6 2 π ) 2
Further simplify the above expression.
m = 22.36 kg
The weight of a body of mass m is given as,
W = m g
By substituting the given value in above equation, we get
W = 22.36 × 9.8 ≈ 219 N
Thus, the weight of the body is 219 N .
Given: The scale of spring balance reads from 0 to
The maximum force exerted on the spring is given as,
Where, the maximum mass that the scale can read is
By substituting the given values in above equation, we get
The spring force of the balance is given as,
Where, the spring force is
By substituting the given values in above equation, we get
The time period of oscillation is given as,
Where, the time period of oscillation is
By substituting the given values in above equation, we get
Further simplify the above expression.
The weight of a body of mass
By substituting the given value in above equation, we get
Thus, the weight of the body is
