a particle 100g attach with a horizontal spring moving s.h.m.with amplitude 5cm .when this particle is passes through mid point a small particle placed on it then both moving s.h.m.with amplitude 4cm.find the mass of small particle .
To find the mass of the small particle, we need to analyze the given information.
Given:
- Mass of the larger particle (attached to the spring): 100 g
- Amplitude of the larger particle's simple harmonic motion (SHM): 5 cm
- Amplitude of the small particle's SHM (when placed on the larger particle): 4 cm
Let's assume the larger particle has a mass of M and the small particle has a mass of m.
In simple harmonic motion, the period is determined by the mass attached to the spring. Therefore, the period of both the larger and small particles will be the same.
The period of simple harmonic motion is given by T = 2π√(m/k), where T is the period, m is the mass of the particle, and k is the spring constant.
Since the period remains the same when the small particle is placed on the larger particle, we have:
2π√(m/k) = 2π√(M/k)
Simplifying the equation:
√(m/k) = √(M/k)
Squaring both sides of the equation:
m/k = M/k
Canceling out the k terms:
m = M
Substituting the given mass of the larger particle (M = 100 g):
m = 100 g
Therefore, the mass of the small particle is also 100 g.