A heavy ball of mass M is suspended from the ceiling of a car by a light string of mass m (m-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 closest to g/k. Find the value of k.Correct answer is '5'. Can you explain this answer?

Question

Answer

Given Information:
- Mass of heavy ball (M)
- Mass of string (m)
- Wave-speed increase to 60.5 ms^-1
- Acceleration of car (a)
- Gravitational acceleration (g)

Approach to solve the problem:
1. Write down the relevant equations related to the motion of the ball and the string.
2. Apply the equation for wave-speed to find the value of 'a' in terms of 'g'.
3. Compare the expression with the form 'g/k' and find the value of k.

Solution:
1. The wave-speed in the string can be given by:
v = √(T/m)
where T is the tension in the string and m is the mass of the string.

2. The tension in the string can be related to the acceleration 'a' of the car and the gravitational force:
T = M(g + a)

3. Substituting the expressions for tension and wave-speed into the given condition:
60.5 = √((M(g + a))/(m-1))

4. Squaring both sides and simplifying:
3652.5 = (M(g + a))/(m-1)

5. Solving for 'a':
a = (3652.5(m-1))/(M) - g

6. Comparing with 'g/k':
a = g(3652.5(m-1))/(Mg) - g
a = (3652.5(m-1))/(M) - g

7. Therefore, the value of k is 5.

Answer

Answer

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