The surface of water in a water tank of cross section area 750 cm 2 on the top of a house is h m above the tap level. The speed of water coming out through the tap of cross section area 500 mm 2 is 30 cm / s. At that instant, (d h/d t) is x × 10-3 m / s. The value of x will be

Question

The surface of water in a water tank of cross section area 750 cm 2 on the top of a house is h m above the tap level. The speed of water coming out through the tap of cross section area 500 mm 2 is 30 cm / s. At that instant, (d h/d t) is x × 10-3 m / s. The value of x will be  (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

A 1 V 1= A 2 V 2 750 × 10-4 V 1=500 × 10-6 × 0.3 V 1=(500 × 3 × 10-3/750) m / s =2 × 10-3 m / s ( dh / dt )=-2 × 10-3 m / s

Q. The surface of water in a water tank of cross section area 750cm2 on the top of a house is hm above the tap level. The speed of water coming out through the tap of cross section area 500mm2 is 30cm/s. At that instant, dtdh​ is x×10−3m/s. The value of x will be ____

A1​V1​=A2​V2​ 750×10−4V1​=500×10−6×0.3 V1​=750500×3×10−3​m/s =2×10−3m/s dtdh​=−2×10−3m/s

$A_{1} V_{1} = A_{2} V_{2}$
$750 \times 1 0^{- 4} V_{1} = 500 \times 1 0^{- 6} \times 0.3$
$V_{1} = \frac{500 \times 3 \times 1 0 ^{- 3}}{750} m / s$
$= 2 \times 1 0^{- 3} m / s$
$\frac{d h}{d t} = - 2 \times 1 0^{- 3} m / s$