AP EAPCET 24-Aug-2021 Shift 2 Paper

From graph, the force is varying sinusoidally with time by equation,
F=−2.cos‌ω‌t ...(i)
where, ω be the angular frequency of variation of force.
Since, the graph is completing one cycle in 8s, hence time period, T=8s
Using expression of change of momentum.
Δn=∫n8Fdt=∫n8−2‌cos‌ω‌t‌d‌t [from Eq. (i)]
=−

2

ω

[sin‌ω‌t]38
=

−2

ω

[sin‌ω‌8−sin‌0]
=

−2

ω

[sin‌

2π

8

‌8−0] (∵ω=

2π

T

)
=

−2

ω

[sin‌2‌π]=0 [∵sin‌0=sin‌2‌π=0]
Hence, the gain or change of linear momentum is zero.