a small sphere of mass m is suspended by a string from the ceiling of a car . if the car begins to move with a constant acceleration g/2 , then the tension in the string is ?????? ?
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Answer:
Since, there is movement of the car, the string will accelerate thereby making some angles . let θ be the angles made by the string while moving from its original position to displaced position. On resolving the tension T, when it makes since and cosine components.
Vertical component is given by ,
Tcosθ=mg−−−(1)
Horizontalcomponentis
Tsinθ=ma−−−(2)
Squaringandadding(1)+(2).
T
2
cos
2
θ+T
2
sin
2
θ=m
2
a
2
+m
2
g
2
T
2
(cos
2
θ+sin
2
θ)=m
2
(a
2
+g
2
)
T
2
=m
2
(a
2
+g
2
)
T=m
(a
2
+g
2
)
Hence,optionDisthecorrectanswer.
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