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Figure shows a small block suspended vertically using an ideal spring. Initially spring is in natural lenght and the mass is 1 mm above the principal axis of a concave mirror whose focal lenght is 20 cm. given the mass m=10grams, k=100N/m, g=10
, the amplitude of the image of the block formed by concave mirror is A millimetres, find the integer value "A".
Asked by ggroy | 18 Mar, 2019, 19:27: PM
Expert Answer
Relevant informations are missing. It is not mentioned explicitly the mass loaded spring is oscillating or the mass is simply hanging.
It is mentioned that "amplitude of image", hence it is assumed the mass attached to spring is oscillating.
if force constant is 100N/m, then 10g mass is giving a force = 10×10-3 ×10 = 0.1 N hence spring is extended by 1 mm.
Hence we assume the amplitude of vibration of object mass is 1 mm.
Now another missing information is distance between mirror and the oscillating mass.
Let us assume the mirror is placed at a distance 30 cm from the mass-spring system.
We have mirror formula : (1/u) + (1/v) = 1/f ................(1)
where u = mirror to object distance = 30 cm assumed.
v = mirror to image distance
f = focal length of mirror = 20 cm (given)
using the values of u and f in eqn.(1), we get mirror-to-image distance : (1/v) = (1/f) -(1/u) = (1/20) - (1/30) = 1/60 or v = 60 cm.
magnification = -v/u = -60/20 = -3
Hence amplitude of vibrating image is 3 mm
Answered by Thiyagarajan K | 18 Mar, 2019, 23:18: PM
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