A boy is hanging over a pulley inside a car through a string. The second end of the string is in the hand of a person standing in the car. The car is moving with constant acceleration 'a' Directed horizontally as shown in figure. Other end of the string is pulled with constant acceleration 'a' (relative to car) vertically. The tension in the string is equal to

Question

A boy is hanging over a pulley inside a car through a string. The second end of the string is in the hand of a person standing in the car. The car is moving with constant acceleration 'a' Directed horizontally as shown in figure. Other end of the string is pulled with constant acceleration 'a' (relative to car) vertically. The tension in the string is equal to <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-ng4ryrz8ytilaolm.jpg" /> (A) m√g2 + a2 (B) m√g2 + a2-ma (C) m√g2 + a2+ma (D) m(.g+a.)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-ng4ryrz8ytiluxpy.jpg" /> (Force diagram in the frame of the car) Applying Newton's law perpendicular to string mgsinθ =macosθ ⇒ tanθ =(a/g) Applying Newton's law along string ⇒ T-m√g2 + a2=ma/T=m√g2 + a2+ma

$m g^{2} + a^{2}$

$m g^{2} + a^{2} - ma$

$m g^{2} + a^{2} + ma$

$m (g + a)$

(Force diagram in the frame of the car)
Applying Newton's law perpendicular to string $m g s in θ = ma cos θ \Rightarrow t an θ = \frac{a}{g}$
Applying Newton's law along string $\Rightarrow T - m g^{2} + a^{2} = ma / T = m g^{2} + a^{2} + ma$

mg2+a2​

mg2+a2​−ma

mg2+a2​+ma

m(g+a)

(Force diagram in the frame of the car) Applying Newton's law perpendicular to string mgsinθ=macosθ⇒tanθ=ga​ Applying Newton's law along string ⇒T−mg2+a2​=ma/T=mg2+a2​+ma

$m g^{2} + a^{2}$

$m g^{2} + a^{2} - ma$

$m g^{2} + a^{2} + ma$

$m (g + a)$

(Force diagram in the frame of the car)
Applying Newton's law perpendicular to string $m g s in θ = ma cos θ \Rightarrow t an θ = \frac{a}{g}$
Applying Newton's law along string $\Rightarrow T - m g^{2} + a^{2} = ma / T = m g^{2} + a^{2} + ma$