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Pressure(numerical problem) (Numerical Problem)

Q. A girl of mass 30kg whose feet covered 150cm2 on ground. Find the pressure on ground? Soln→ Mass of girl m = 30kg Acceleration due to gravity g = 9.8 m/sec Weight or force F = m g = 30 × 9.8 = 294 N Area (A) = 150cm2 = $\frac{\mathrm{150}}{\mathrm{100\; \times \; 100}}$ m 2 = 1.5 × 10 − 2 m2 By the formula, P = $\frac{F}{A}$ = $\frac{\mathrm{294}}{\mathrm{1.5\; \times \; 10<sup>\; -\; 2</sup>\; m<sup>2</sup>}}$ = 196 × 102 = 19600 Pa = 1.96 × 104Pa.	Q. A wooden block of 20cm, 15cm and 10cm is of density 0.8 gm/cm3 is floating on water of density 1 gm/cm3. Answer these questions: Volume of wooden block mass of wooden block dispalced water height of wooden block outside the water Soln→1. Volume of wooden block V = l × b × h = 20 × 15 × 10 = 3000 cm3 2. mass of wooden block m = v × d = 3000 × 0.8 = 2400 gm 3. Displaced water mass = mass of wooden block = 2400 gm 4. Fraction of block outside the water = 1 − $\frac{\mathrm{density\; of\; block}}{\mathrm{density\; of\; water}}$ = 1 − $\frac{\mathrm{0.8}}{1}$= 1 − $\frac{8}{\mathrm{10}}$ = 1 −$\frac{4}{5}$ = $\frac{\mathrm{5\; -\; 4}}{5}$ = $\frac{1}{5}$ Height of block outside the water = $\frac{\mathrm{density\; of\; block}}{\mathrm{density\; of\; water}}$ × h = $\frac{1}{5}$ × 10 = 2 cm
Q. An ice of dimension (50cm, 30cm and 20cm). When this ice is put on water what will be the displaced water? [density of ice 0.92 gm/cm3 and density of water 1 gm/m3.] Soln→ Ice Volume V = 50 × 30 × 20 = 30000 cm3 Ice density d1 = 0.92 gm/cm3 Ice mass m = v × d1 = 30000 × 0.92 = 27600 gm Displaced water mass (m) = mass of Ice = 27600 gm = 27.6 kg Water density d2 = 1 gm/cm3 Volume of displaced water v = $\frac{m}{\mathrm{d<sub>2</sub>}}$ = $\frac{\mathrm{27600}}{1}$ = 27600 cm3 Q. An iceberg of base area 1000cm3 and height 30cm is floating on water, find the displaced water? [density of ice 0.92 gm/cm3 and density of water 1 gm/m3.]	Q. A wooden block of volume 1.6 m3 and density 800 kg/m3 is floating on water of density 1000 kg/m3. Find the fraction of wooden block inside the water? Soln→ Volume of wooden block (V) = 1.6 m3 Density of wood d1 = 800 kg/m3 Density of water d2 = 1000 kg/m3 Fraction of block inside the water = $\frac{\mathrm{d<sub>1</sub>}}{\mathrm{d<sub>2</sub>}}$ = $\frac{\mathrm{800}}{\mathrm{1000}}$ =$\frac{4}{5}$ Q. Wooden block of density 800 kg/m3 is floating on water such that out of 5 part 4 part is inside the water. If so find the density of water?
Q.A tank of lenght 3 m weidth 2 m and height 1m is half filled with. Find the pressure on bottom of tank? Soln→ Depth of water = $\frac{1}{2}$ m water density (d) 1000 kg/m3 acceleration (g) 9.8 m/sec2 pressure on bottom of tank p = ? By the formula, P = h d g = $\frac{1}{2}$ × 1000 × 9.8 = 4900 pa.	Q.1 kg brick is put into water then find the dispalced water? [density of brick is 2.5gm/cm3 and density of water is 1gm/cm3.] Soln→ Mass of brick (m) = 1kg = 1000gm density of brick d1 = 2.5gm/cm3 By the formula, Volume of brick (V) = $\frac{\mathrm{mass\; of\; brick(m)}}{\mathrm{density\; of\; brick\; d<sub>1</sub>}}$ = $\frac{\mathrm{1000}}{\mathrm{2.5}}$ = 400cm3 Volume of displaced water = Volume of brick = 400 cm3 Volumeof displaced water (V) = 400 cm3 Density of water d2 = 1 gm/cm3 Mass of water (m) = v × d2 =400 × 1 =400 gm mass of water m = 400 gm.
Q.A hydrometer show density of liquid 1000 kg/m3. Volume of hydrometer immersed in liquid 5 × 10 − 5 m3 find the weight of hydrometer? Soln→ Density of liquid (d) = 1000 km/m3 Volume of displaced liquid (V) = 5 × 10 − 5 m3 Acceleration (g) = 10 m/sec2 Weight of Displaced liquid (w) = v d g = 5 × 10 − 5 × 1000 × 10 = 0.5 N According to Plawan's law, On floating condition, weight of hydrometer = weight of displaced liquid Therefor, weight of hydrometer = 0.5 N	Q.What should be height of water in a tank such that pressure on bottom of water tank is equal to pressure on bottom of 5m height mercury tank? [Density of mercury is 13600kg/m3 and density of water is 1000kg/m3.] Soln→ Height of mercury h1 = 5 m density of mercury d1 13600 kg/m3 density of water d2 = 10000 kg/m3 height of water h2 = ? According to question, Pressure due to mercury = pressure due to water or, h1 d1 g = h2 d2 g or, 5 × 13600 × 9.8 = h2 × 1000 × 9.8 or, h = 68m Height of water h2 = 68m