If the length of a pendulum is made 9 times and mass of the bob is made 4 times, then the value of time period becomes :

Question

If the length of a pendulum is made 9 times and mass of the bob is made 4 times, then the value of time period becomes : (A)  3T  (B)  3/2T  (C)  4T  (D)  2T

Tardigrade Admin · Accepted Answer

Time period T=2 π √(l/g) i.e., time period does not depend on the mass of the bob. ∴ T propto √l (T1/T2)=√(l1/l2) ⇒ (T/T2)=√(l/9 l) ∴ T2=3 T

Q. If the length of a pendulum is made $9$ times and mass of the bob is made $4$ times, then the value of time period becomes :

$3 T$

$3/2 T$

$4 T$

$2 T$

Time period $T = 2 π \frac{l}{g}$
i.e., time period does not depend on the mass of the bob.
$∴ T \propto l$
$\frac{T _{1}}{T _{2}} = \frac{l _{1}}{l _{2}}$
$\Rightarrow \frac{T}{T _{2}} = \frac{l}{9 l}$
$∴ T_{2} = 3 T$

Q. If the length of a pendulum is made 9 times and mass of the bob is made 4 times, then the value of time period becomes :

3T

3/2T

4T

2T