Obtain in expression for the time period T of a simple pendulun. The time period depend upon (i) mass 'm' of the bob (ii) length 'l' of the pendulum and (iii) acceieration due to gravity g at the place where the pendulum is suspended. (Constant k = 2pi ) i.e.

Obtain in expression for the time period T of a simple pendulun. The t

1.	Obtain in expression for the time period T of a simple pendulun. The time period depend upon (i) mass 'm' of the bob (ii) length 'l' of the pendulum and (iii) acceieration due to gravity g at the place where the pendulum is suspended. (Constant k = 2pi ) i.e.
Answer» <html><body><p></p>Solution :`Tproptom^(a)l^(<a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a>)g^(c),""T=<a href="https://interviewquestions.tuteehub.com/tag/k-527196" style="font-weight:bold;" target="_blank" title="Click to know more about K">K</a>.m^(a)l^(b)g^(c)` <br/> Here k is the dimensionless constant. <br/> Rewriting the above equation with dimensions. <br/> `[T^(1)]=[M^(a)][L^(b)][LT^(-2)]^(c)` <br/> `[M^(0)L^(0)T^(1)]=[M^(a)L^(b+c)T^(-2c)]` <br/> Comparing the <a href="https://interviewquestions.tuteehub.com/tag/powers-1162174" style="font-weight:bold;" target="_blank" title="Click to know more about POWERS">POWERS</a> of M, L and T on both sides, <br/> `a=0, b+c=0, -2c=1` <br/> <a href="https://interviewquestions.tuteehub.com/tag/solving-1217196" style="font-weight:bold;" target="_blank" title="Click to know more about SOLVING">SOLVING</a> for a, b and c, we get `a=0, b=1//2, " and " c=-1//2` <br/> From the above equation `T=k.m^(0)l^(1//2)g^(-1//2)` <br/> `T=k(1/g)^(1//2)=ksqrt(1//g)` <br/> Experimentally `k=2pi`, hence `T=2pisqrt(l//g)`</body></html>