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(C) To find the tension in the string,we analyze the forces acting on the bob of mass $m$ in the non-inertial frame of the car.In the car's frame,the

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

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(C) To find the tension in the string,we analyze the forces acting on the bob of mass $m$ in the non-inertial frame of the car.In the car's frame,the bob experiences a gravitational force $mg$ downwards and a pseudo force $ma$ horizontally backwards.The effective acceleration due to gravity in this frame is $g_{eff} = \sqrt{g^2+a^2}$.The component of the effective weight acting along the string is $m g_{eff} = m \sqrt{g^2+a^2}$.Since the string is being pulled with an acceleration '$a$' vertically,the bob also experiences an upward acceleration '$a$' relative to the car.Applying Newton's second law along the direction of the string:$T - m \sqrt{g^2+a^2} = ma$Therefore,the tension in the string is $T = m \sqrt{g^2+a^2} + ma$.

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