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  4. 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 />

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Q. 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

NTA AbhyasNTA Abhyas 2022

Solution:

Solution
(Force diagram in the frame of the car)
Applying Newton's law perpendicular to string $mgsin\theta =macos\theta \Rightarrow tan\theta =\frac{a}{g}$
Applying Newton's law along string $\Rightarrow T-m\sqrt{g^{2} + a^{2}}=ma/T=m\sqrt{g^{2} + a^{2}}+ma$