(a) Statement – 1 is true, statement – 2 is true; statement – 2 is the correct explanation of statement – 1.

Question

For the following questions, statement as well as the reason(s) are given. Each questions has four options. Select the correct option. 

(a) Statement – 1 is true, statement – 2 is true; statement – 2 is the correct explanation of statement – 1. 

(b) Statement – 1 is true, statement – 2 is true but statement – 2 is not the correct explanation of statement – 1. 

(c) Statement – 1 is true, statement – 2 is false 

(d) Statement – 1 is false, statement – 2 is true 

(A) a 

(B) b 

(C) c 

(D) d 

Statement – 1 : For small amplitude, the motion of a simple pendulum is a S.H.M. with periodic time T = 2π √(ℓ/g). For large amplitudes, periodic time is greater than 2π √(ℓ/g). 

Statement – 2 : For large amplitude, the speed of the bob is more when it passes through the mid-point (equilibrium point). 

(A) a 

(B) b 

(C) c 

(D) d

Answer 1

The correct option (b) Statement – 1 is true, statement – 2 is true but statement – 2 is not the correct explanation of statement – 1.

Explanation:

restoring force = F = – mgsinθ

F = – mg_e

where ge = g sinθ

as θ is small ge = gθ

For large oscillation, g sinθ < gθ (as sin θ < 0)

∴ T > 2π √(ℓ/g)

hence statement 1 is true.

also for large amplitudes, the speed of bob is more when it passes through the midpoint. Hence both statements are true but statement 2 is not explanation of 1.