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Two identical springs have the same force constant 73.5Nm1 . The elongation produced in each spring in three cases shown in figure (a), figure (b), and figure (c). ( g=9.8ms2 ):
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(A) 16m,23m,13m
(B) 13m,13m,13m
(C) 23m,13m,16m
(D) 13m,23m,23m

Answer
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Hint :Here, the spring constant is given and we have to find the elongation produced in each spring. To find elongation we have to find the resultant of each spring constant in each figure with weight hanging on the spring due to which elongation is possible.

Complete Step By Step Answer:
Here, the spring constant is 73.5Nm1 and let us denote it as k .
Now, let us first consider the figure (a), the effective spring constant is given by:
Let effective spring constant be k1
 k1=k+k
 k1=2k=2(73.5)=147Nm1
In figure (a), the elongation in the spring, is given by
Let us consider elongation in figure (a) as y1
 y1=mgk=5×9.8147=13
 y1=13m
Now, in figure (b), let us find the effective spring constant of the springs given in the above figure.
Let effective spring constant be k2 , it is given by:
 k2=k×kk+k=k22k=k2=73.52Nm1
The elongation of the spring be y2 in figure (b) as
 y2=5×9.8×273.5=23
 y2=23m
Now, in figure (c), the effective spring constant is as follows:
Let k3 be the effective spring constant in figure (c),
 k3=k=73.5Nm1
The elongation of the spring be y3 in figure (c)
 y3=5×9.873.5=23m
 y3=23m
Thus, we have concluded that the elongations in the figures with springs and given spring constant is as follows 13m,23m,23m respectively.
The correct answer is option D.

Note :
Here, we have been given the spring constant of springs in the above figures using that we calculated the effective spring constant and found their elongations in each figure. The elongation is calculated by using formula yE = l0 + mgk
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