6. The time t, of a complete oscillation of a simplependulam of lenght

1.	6. The time t, of a complete oscillation of a simplependulam of lenght ' is given by the equationT 2T,la where "g' is a gravitational constantfind approximate percentage error in 'T whenthe percentage of error in .1, is 1%
Answer» T = 2π√1/g →Δl/l× 100 = 1 (Given) Here we are using Percentage error formula dy/y×100 (OR) dx/x×100 → dl/l× 100 = 1 → T = 2π√1/g → T = 2π(l/g)¹/² Now, Apply Log on Both sides → logT = log2π(l/g)¹/² → logT - log2π + log(l/g)¹/² → logT = log2π + 1/2log(l/g) → logT = log2π + 1/2[log l - log g ] → log T = log 2π + 1/2log l - 1/2log g → 1/T× dt = 0 + 1/2× 1/l - 1/2× (0) → 1/T× dt = 1/2 dl/l → dT/T = 1/2 dl/l → dT/T× 100 = 1/2 dl/l× 100 { Apply Percentage error formula } → dT/T× 100 = 1/2 % { FINAL ANSWER }

6. The time t, of a complete oscillation of a simplependulam of lenght ' is given by the equationT 2T,la where "g' is a gravitational constantfind approximate percentage error in 'T whenthe percentage of error in .1, is 1%

Answer»

T = 2π√1/g

→Δl/l× 100 = 1 (Given) Here we are using Percentage error formula dy/y×100 (OR) dx/x×100 → dl/l× 100 = 1

→ T = 2π√1/g

→ T = 2π(l/g)¹/²

Now, Apply Log on Both sides

→ logT = log2π(l/g)¹/²

→ logT - log2π + log(l/g)¹/²

→ logT = log2π + 1/2log(l/g)

→ logT = log2π + 1/2[log l - log g ]

→ log T = log 2π + 1/2log l - 1/2log g

→ 1/T× dt = 0 + 1/2× 1/l - 1/2× (0)

→ 1/T× dt = 1/2 dl/l

→ dT/T = 1/2 dl/l

→ dT/T× 100 = 1/2 dl/l× 100 { Apply Percentage error formula }

→ dT/T× 100 = 1/2 % { FINAL ANSWER }