JEE Main 31-Aug-2021 Shift 1 Solved Paper

Given,
Angle of inclination, θ = 30º
Acceleration, a=10ms−2
Acceleration due to gravity, g=10ms−2
According to the question the car and bob is as shown below, Here, F'is the pseudo force acting on the bob when we considered it from car’s frame and T is the tension on the string.
In equilibrium, ΣFx=0 and ΣFy=0
⇒F′‌cos‌30°=T‌sin‌α
ma‌cos‌30°‌sin‌α=T ...(i)
where, m is the mass of the bob.
F′‌sin‌30°+mg=T‌cos‌α
⇒ma‌sin‌30°+mg=

ma‌cos‌30°

sin‌α

(cos‌α) [∵ using Eq. (i)]
⇒a‌sin‌30°+g=

a‌cos‌30°

sin‌α

(cos‌α)
10×

1

2

+10=

10×√3

2

.α
⇒

1

2

+1=

√3

2

.α
⇒

3

2

=

√3

2

.α
orcot‌α=√3
⇒α=30°