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GRADE 10 PRACTICE

Physics Problems: Hydrostatics, Grade 10

Pressure, density and buoyant force.

12 problems across 2 sub-topics
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Problem statements

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12 problems
Position in this set: 1 from 12

Problem #171

Pressure in liquids and gases

Liquid density 1000 kg/m³, depth 0{,}5 m. Find the excess pressure at this depth at g = 10 N/kg.

Answer options

  1. 5000\,\text{Па}
  2. 10000\,\text{Па}
  3. 2500\,\text{Па}
  4. 15000\,\text{Па}
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Given
r
1000\,\text{кг/м}^{3}
h
0{,}5\,\text{м}
g
10\,\text{Н/кг}
Find

p

  1. p=\rho ghp=1000 \cdot 10 \cdot 0{,}5p=5000\,\text{Па}

    We calculate only the pressure of the liquid without atmospheric pressure.

Answer5000\,\text{Па}

Position in this set: 2 from 12

Problem #172

Pressure in liquids and gases

Liquid density 800 kg/m³, depth 0{,}8 m. Find the excess pressure at this depth at g = 10 N/kg.

Answer options

  1. 12800\,\text{Па}
  2. 6400\,\text{Па}
  3. 3200\,\text{Па}
  4. 19200\,\text{Па}
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Given
r
800\,\text{кг/м}^{3}
h
0{,}8\,\text{м}
g
10\,\text{Н/кг}
Find

p

  1. p=\rho ghp=800 \cdot 10 \cdot 0{,}8p=6400\,\text{Па}

    We calculate only the pressure of the liquid without atmospheric pressure.

Answer6400\,\text{Па}

Position in this set: 3 from 12

Problem #173

Pressure in liquids and gases

The excess water pressure is 24 kPa. Density of water 1000 kg/m³, g = 10 N/kg. Find the depth.

Answer options

  1. 4{,}8\,\text{м}
  2. 2{,}4\,\text{м}
  3. 1{,}2\,\text{м}
  4. 7{,}2\,\text{м}
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Given
p
24\,\text{кПа}
r
1000\,\text{кг/м}^{3}
g
10\,\text{Н/кг}
Find

h

  1. P=1000pP=24 \cdot 1000P=24000\,\text{Па}

    We reduce pressure to SI.

  2. h=\frac{P}{\rho g}h=\frac{24000}{(1000 \cdot 10)}h=2{,}4\,\text{м}

    We express the depth from the law of hydrostatics.

Answer2{,}4\,\text{м}

Position in this set: 4 from 12

Problem #174

Pressure in liquids and gases

The excess water pressure is 35 kPa. Density of water 1000 kg/m³, g = 10 N/kg. Find the depth.

Answer options

  1. 7\,\text{м}
  2. 1{,}75\,\text{м}
  3. 3{,}5\,\text{м}
  4. 10{,}5\,\text{м}
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Given
p
35\,\text{кПа}
r
1000\,\text{кг/м}^{3}
g
10\,\text{Н/кг}
Find

h

  1. P=1000pP=35 \cdot 1000P=35000\,\text{Па}

    We reduce pressure to SI.

  2. h=\frac{P}{\rho g}h=\frac{35000}{(1000 \cdot 10)}h=3{,}5\,\text{м}

    We express the depth from the law of hydrostatics.

Answer3{,}5\,\text{м}

Position in this set: 5 from 12

Problem #175

Pressure in liquids and gases

In a vessel above water height 0{,}3 m is the oil height 0{,}2 m. Densities of water and oil 1000 and 800 kg/m³. Find the excess pressure at the bottom; g = 10 N/kg.

Answer options

  1. 9200\,\text{Па}
  2. 2300\,\text{Па}
  3. 4600\,\text{Па}
  4. 13800\,\text{Па}
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Given
h_1
0{,}3\,\text{м}
h_2
0{,}2\,\text{м}
r_1
1000\,\text{кг/м}^{3}
r_2
800\,\text{кг/м}^{3}
g
10\,\text{Н/кг}
Find

p

  1. p_1=\rho_1 gh_1p_1=1000 \cdot 10 \cdot 0{,}3p_1=3000\,\text{Па}

    We consider the contribution of the water layer.

  2. p_2=\rho_2 gh_2p_2=800 \cdot 10 \cdot 0{,}2p_2=1600\,\text{Па}

    We calculate the contribution of oil.

  3. p=p_1+p_2p=3000 + 1600p=4600\,\text{Па}

    The pressures of the layers add up.

Answer4600\,\text{Па}

Position in this set: 6 from 12

Problem #176

Pressure in liquids and gases

In a vessel above water height 0{,}5 m is the oil height 0{,}4 m. Densities of water and oil 1000 and 800 kg/m³. Find the excess pressure at the bottom; g = 10 N/kg.

Answer options

  1. 16400\,\text{Па}
  2. 4100\,\text{Па}
  3. 24600\,\text{Па}
  4. 8200\,\text{Па}
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Given
h_1
0{,}5\,\text{м}
h_2
0{,}4\,\text{м}
r_1
1000\,\text{кг/м}^{3}
r_2
800\,\text{кг/м}^{3}
g
10\,\text{Н/кг}
Find

p

  1. p_1=\rho_1 gh_1p_1=1000 \cdot 10 \cdot 0{,}5p_1=5000\,\text{Па}

    We consider the contribution of the water layer.

  2. p_2=\rho_2 gh_2p_2=800 \cdot 10 \cdot 0{,}4p_2=3200\,\text{Па}

    We calculate the contribution of oil.

  3. p=p_1+p_2p=5000 + 3200p=8200\,\text{Па}

    The pressures of the layers add up.

Answer8200\,\text{Па}

Position in this set: 7 from 12

Problem #177

Density and buoyant force

The body has supplanted 0{,}002 m³ liquid density 1000 kg/m³. Find the Archimedes force at g = 10 N/kg.

Answer options

  1. 40\,\text{Н}
  2. 20\,\text{Н}
  3. 10\,\text{Н}
  4. 60\,\text{Н}
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Given
V
0{,}002\,\text{м}^{3}
r
1000\,\text{кг/м}^{3}
g
10\,\text{Н/кг}
Find

F_A

  1. F_A=\rho gVF_A=1000 \cdot 10 \cdot 0{,}002F_A=20\,\text{Н}

    We take the density of the liquid and the displaced volume.

Answer20\,\text{Н}

Position in this set: 8 from 12

Problem #178

Density and buoyant force

The body has supplanted 0{,}003 m³ liquid density 800 kg/m³. Find the Archimedes force at g = 10 N/kg.

Answer options

  1. 48\,\text{Н}
  2. 12\,\text{Н}
  3. 24\,\text{Н}
  4. 72\,\text{Н}
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Given
V
0{,}003\,\text{м}^{3}
r
800\,\text{кг/м}^{3}
g
10\,\text{Н/кг}
Find

F_A

  1. F_A=\rho gVF_A=800 \cdot 10 \cdot 0{,}003F_A=24\,\text{Н}

    We take the density of the liquid and the displaced volume.

Answer24\,\text{Н}

Position in this set: 9 from 12

Problem #179

Density and buoyant force

Dynamometer shows 30 H in the air and 20 H when the body is completely immersed in water. Density of water 1000 kg/m³, g = 10 N/kg. Find the volume of the body.

Answer options

  1. 0{,}002\,\text{м}^{3}
  2. 0{,}0005\,\text{м}^{3}
  3. 0{,}001\,\text{м}^{3}
  4. 0{,}003\,\text{м}^{3}
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Given
P_1
30\,\text{Н}
P_2
20\,\text{Н}
r
1000\,\text{кг/м}^{3}
g
10\,\text{Н/кг}
Find

V

  1. F_A=P_1-P_2F_A=30 - 20F_A=10\,\text{Н}

    The decrease in reading is equal to the buoyancy force.

  2. V=\frac{F_A}{\rho g}V=\frac{10}{(1000 \cdot 10)}V=0{,}001\,\text{м}^{3}

    The immersion is complete, so the displaced volume is equal to the volume of the body.

Answer0{,}001\,\text{м}^{3}

Position in this set: 10 from 12

Problem #180

Density and buoyant force

Dynamometer shows 50 H in the air and 30 H when the body is completely immersed in water. Density of water 1000 kg/m³, g = 10 N/kg. Find the volume of the body.

Answer options

  1. 0{,}004\,\text{м}^{3}
  2. 0{,}001\,\text{м}^{3}
  3. 0{,}006\,\text{м}^{3}
  4. 0{,}002\,\text{м}^{3}
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Given
P_1
50\,\text{Н}
P_2
30\,\text{Н}
r
1000\,\text{кг/м}^{3}
g
10\,\text{Н/кг}
Find

V

  1. F_A=P_1-P_2F_A=50 - 30F_A=20\,\text{Н}

    The decrease in reading is equal to the buoyancy force.

  2. V=\frac{F_A}{\rho g}V=\frac{20}{(1000 \cdot 10)}V=0{,}002\,\text{м}^{3}

    The immersion is complete, so the displaced volume is equal to the volume of the body.

Answer0{,}002\,\text{м}^{3}

Position in this set: 11 from 12

Problem #181

Density and buoyant force

Body mass 2 kg and volume 500 cm³ completely immersed in a liquid with a density 1000 kg/m³ and hangs on the dynamometer. Find his testimony; g = 10 N/kg.

Answer options

  1. 30\,\text{Н}
  2. 7{,}5\,\text{Н}
  3. 45\,\text{Н}
  4. 15\,\text{Н}
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Given
m
2\,\text{кг}
V
500\,\text{см}^{3}
r
1000\,\text{кг/м}^{3}
g
10\,\text{Н/кг}
Find

P

  1. v=\frac{V}{10^6}v=\frac{500}{1000000}v=0{,}0005\,\text{м}^{3}

    Convert cubic centimeters to cubic meters.

  2. F_A=\rho gvF_A=1000 \cdot 10 \cdot 0{,}0005F_A=5\,\text{Н}

    We find the buoyant force.

  3. P=mg-F_AP=2 \cdot 10 - 5P=15\,\text{Н}

    The dynamometer maintains the difference between gravity and the Archimedes force.

Answer15\,\text{Н}

Position in this set: 12 from 12

Problem #182

Density and buoyant force

Body mass 3 kg and volume 800 cm³ completely immersed in a liquid with a density 800 kg/m³ and hangs on the dynamometer. Find his testimony; g = 10 N/kg.

Answer options

  1. 23{,}6\,\text{Н}
  2. 47{,}2\,\text{Н}
  3. 11{,}8\,\text{Н}
  4. 70{,}8\,\text{Н}
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Given
m
3\,\text{кг}
V
800\,\text{см}^{3}
r
800\,\text{кг/м}^{3}
g
10\,\text{Н/кг}
Find

P

  1. v=\frac{V}{10^6}v=\frac{800}{1000000}v=0{,}0008\,\text{м}^{3}

    Convert cubic centimeters to cubic meters.

  2. F_A=\rho gvF_A=800 \cdot 10 \cdot 0{,}0008F_A=6{,}4\,\text{Н}

    We find the buoyant force.

  3. P=mg-F_AP=3 \cdot 10 - 6{,}4P=23{,}6\,\text{Н}

    The dynamometer maintains the difference between gravity and the Archimedes force.

Answer23{,}6\,\text{Н}

The theory behind these problems

Work through the topic if a problem will not give in.

Pressure in liquids and gasesPressure due to force, atmospheric pressure and hydrostatic pressure.Density and buoyant forceDensity, buoyant force and floating bodies.

Formulas by topic

Look up symbols and units of measurement in the reference.

Pressurep · ПаDensityρ · кг/м³