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» Solution :`Tproptom^(a)l^(B)g^(c),""T=K.m^(a)l^(b)g^(c)` Here k is the dimensionless constant. Rewriting the above equation with dimensions. `[T^(1)]=[M^(a)][L^(b)][LT^(-2)]^(c)` `[M^(0)L^(0)T^(1)]=[M^(a)L^(b+c)T^(-2c)]` Comparing the POWERS of M, L and T on both sides, `a=0, b+c=0, -2c=1` SOLVING for a, b and c, we get `a=0, b=1//2, " and " c=-1//2` From the above equation `T=k.m^(0)l^(1//2)g^(-1//2)` `T=k(1/g)^(1//2)=ksqrt(1//g)` Experimentally `k=2pi`, hence `T=2pisqrt(l//g)`