Question

A barometer kept in an elevator reads 76 cm when it is at rest. If the elevator goes up with increasing speed, the reading will be

• A. zero
• B. 76 cm
• C. < 76 cm
• D. > 76 cm

Answer 1

The correct option is C

< 76 cm

Consider the barometer kept in an elevator going upwards with an acceleration a0 as shown, Consider two points A and B as the topmost and bottom most point of barometer column containing mercury. Consider the area of tube to be $\Delta$s Free body diagram of cylinder containing A & B

ℓ = length of mercury column from Newton's second law,

$(P_B-P_A)\Delta s-mg=m{a}_0$ Where m=$\Delta$spl$a_0$ $\Rightarrow \Delta s(P_B-P_A)=\Delta spl(a_0+g)$ $P_B-P_A=pl(a_0+g)$ But $P_A=0$ as there is vacuum above point A $P_B=pl(a_0+g)$

But if the lift was not accelerating, then pressure would have been, $P_B=pgl$ Hence the length of mercury column