Question

a small metallic sphere of mass M is suspended from the ceiling of a car accelerating on a horizontal Road with constant acceleration a .The tension in the string attached with metallic sphere is ?

Answer 1

Answer: $T =m\sqrt(a^2 + g^2)$

Since there is movement of the car, the string will accelerate thereby making some angles. Let $\Theta$ be the angle made by the string while moving from its original position to displaced position. On resolving the tension T, when it makes sine and cosine components.

Vertical component is given by,

$T cos \Theta = mg \rightarrow (1)$ (it is influenced by force of gravity g)

Horizontal component is,

$T sin \Theta = ma \rightarrow(2$  (it is influenced by acceleration of the car a)

Squaring and Adding (1) and (2),

$T_2 cos^2 \Theta + T2 sin2 \Theta =m^2a^2 + m^2g^2$

$T_2 (cos^2 \Theta +  sin2 \Theta) =m^2 (a^2 + g^2)$

$T_2 =m^2a^2 + m^2g^2$

$T =m\sqrt(a^2 + g^2)$