A balloon is tied to a block. The mass of the block is 2 kg. The tension of the string between the balloon and the block is 30 N. Due to the wind, the string has an angle $θ$ relative to the vertical direction, cos $θ$ = 4/5 and sin $θ$ = 3/5. Assume the acceleration of gravity is g = 10 m/s². Also assume the block is small so the force on the block from the wind can be ignored. Then the y-component and the y-component of the acceleration a of the block.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

$9 m / s^{2}, 2 m / s^{2}$

$9 m / s^{2}, 12 m / s^{2}$

$18 m / s^{2}, 2 m / s^{2}$

$18 m / s^{2}, 12 m / s^{2}$

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

The magnitude of the force (from the string) is T=30 N
The x-component $= T \sin θ = 30 \times 3 / 5 = 18 N$
They-component $= T \cos θ = 30 \times 4 / 5 = 24 N$
The total force on the block is:
The x-component = 18 N
The y-component $= 24 - m g = 24 - 20 = 4 N$
The x-component of the acceleration $= 18 N / 2 kg = 9 m / s^{2}$
The y-component of the acceleration $= 4 N / 2 kg = 2 m / s^{2}$