Question 1

Question 2A solid silver piece is immersed in water contained in a measuring cylinder. The level of water rises from 50 mL to 62 mL. Find the volume of silver piece.

Accepted Answer

Initial level of water V1 = 50 mLFinal level of water V2 = 62 mLVolume of silver piece = V2 - V1= 62 - 50= 12 mL = 12 cm3So, volume of silver piece = 12 cm3.

Question 2

Question 4A rectangular field is of length 60 m and breadth 35 m. Find the area of the field.

Accepted Answer

Length = 60 mBreadth = 35 mArea of the field = Length x Breadth = 60 m x 35 m = 2100 m2.So, area of the field = 2100 m2.

Question 3

Question 6A piece of brass of volume 30 cm3 has a mass of 252 g. Find the density of brass in:(i) g cm-3(ii) kg m-3

Accepted Answer

Mass = 252 gVolume = 30 cm-3Density = ?(i) Density=MassVolumeDensity=25230=8.4g cm−3\text{Density} = \dfrac{\text{Mass}}{\text{Volume}} \[1em] \text{Density} = \dfrac{\text{252}}{\text{30}} = 8.4 \text{g cm}^{-3}Density=VolumeMass​Density=30252​=8.4g cm−3So, Density = 8.4 g cm-3.(ii) 1 g cm-3 = 1000 kg m-38.4 g cm-3 = 8.4 x 1000 = 8400 kg m-3So, Density = 8400 kg m-3.

Question 4

Question 7The mass of an iron ball is 312 g. The density of iron is 7.8 g cm-3. Find the volume of the ball.

Accepted Answer

Mass = 312 gDensity = 7.8 g cm-3Volume = ?Density=MassVolume7.8=312VolumeVolume=3127.8=40cm3\text{Density} = \dfrac{\text{Mass}}{\text{Volume}} \[1em] \text{7.8} = \dfrac{\text{312}}{\text{Volume}} \[1em] \text{Volume} = \dfrac{\text{312}}{\text{7.8}} = 40 \text{cm}^{3}Density=VolumeMass​7.8=Volume312​Volume=7.8312​=40cm3So, volume of the ball is 40 cm3.

Question 5

Question 8A cork has a volume 25 cm3. The density of cork is 0.25 g cm-3. Find the mass of the cork.

Accepted Answer

Volume = 25 cm3Density = 0.25 g cm-3Mass = ?Density=MassVolume0.25=Mass25Mass=0.25×25=6.25g\text{Density} = \dfrac{\text{Mass}}{\text{Volume}} \[1em] \text{0.25} = \dfrac{\text{Mass}}{\text{25}} \[1em] \text{Mass} = 0.25 \times 25 = 6.25 \text{g}Density=VolumeMass​0.25=25Mass​Mass=0.25×25=6.25gSo, mass of the cork is 6.25 g.

Question 6

Question 9The mass of 5 litre of water is 5 kg. Find the density of water in g cm-3.

Accepted Answer

Mass = 5 kgVolume = 5 litreDensity = ?Density=MassVolumeDensity=55=1kg litre−1\text{Density} = \dfrac{\text{Mass}}{\text{Volume}} \[1em] \text{Density} = \dfrac{\text{5}}{\text{5}} = 1 \text{kg litre}^{-1}Density=VolumeMass​Density=55​=1kg litre−1Density = 1 kg litre-11 kg = 1000 g; 1 litre = 1000 cm31 kg litre-1 = 10001000\dfrac{\text{1000}}{\text{1000}}10001000​ = 1 g cm-3So, density of water = 1 g cm-3.

Question 7

Question 10A cubical tank of side 1 m is filled with 800 kg of a liquid. Find:(i) the volume of tank(ii) the density of liquid in kg m-3.

Accepted Answer

Side = 1 m; mass = 800 kg(i) Volume of cubical tank = (side)3 = (1 m)3 = 1 m3So, volume of tank = 1 m3.(ii) Density=MassVolumeDensity=8001=800kg m3\text{Density} = \dfrac{\text{Mass}}{\text{Volume}} \[1em] \text{Density} = \dfrac{\text{800}}{\text{1}} = 800 \text{kg m}^{3}Density=VolumeMass​Density=1800​=800kg m3So, density of liquid = 800 kg m-3.

Question 8

Question 11A block of iron has dimensions 2 m x 0.5 m x 0.25 m. The density of iron is 7.8 g cm-3. Find the mass of the block.

Accepted Answer

Density of iron = 7.8 g cm-31 g cm-3 = 1000 kg m-37.8 g cm-3 = 7.8 x 1000 = 7800 kg m-3Volume of iron = 2 m x 0.5 m x 0.25 m = 0.25 m3Mass = ?Density=MassVolume7800=Mass0.25Mass=7800×0.25=1950kg\text{Density} = \dfrac{\text{Mass}}{\text{Volume}} \[1em] \text{7800} = \dfrac{\text{Mass}}{\text{0.25}} \[1em] \text{Mass} = 7800 \times 0.25 = 1950 \text{kg}Density=VolumeMass​7800=0.25Mass​Mass=7800×0.25=1950kgSo, mass of iron = 1950 kg.

Question 9

Question 12The mass of a lead piece is 115 g. When it is immersed into a measuring cylinder, the water level rises from 20 mL mark to 30 mL mark. Find:(i) the volume of the lead piece,(ii) the density of the lead in kg m-3.

Accepted Answer

(i) Mass = 115 g;Initial volume V1 = 20 mL;Final volume V2 = 30 mL;Volume of lead piece = V2 - V1 = 30 - 20 = 10 mL1 mL = 1 cm310 mL = 10 cm3So, volume of the lead piece = 10 cm3.(ii) Density = ? Density=MassVolumeDensity=11510=11.5g cm3\text{Density} = \dfrac{\text{Mass}}{\text{Volume}} \[1em] \text{Density} = \dfrac{\text{115}}{\text{10}} = 11.5 \text{g cm}^{3}Density=VolumeMass​Density=10115​=11.5g cm31 g cm-3 = 1000 kg m-311.5 g cm-3 = 1000 x 11.5 = 11500 kg m-3So, density of lead = 11500 kg m-3.

Question 10

Question 14A car travels a distance of 15 km in 20 minute. Find the speed of the car in:(i) km h-1(ii) m s-1

Accepted Answer

(i) distance = 15 km; time = 20 min60 min = 1 hr20 min = 2060\dfrac{\text{20}}{\text{60}}6020​ = 13\dfrac{\text{1}}{\text{3}}31​ hSpeed=distancetime=1513=15×3=45km h−1\text{Speed} = \dfrac{\text{distance}}{\text{time}} \[1em] = \dfrac{15}{\dfrac{1}{3}} \[1em] = 15 \times 3 \[1em] = 45 \text{km h}^{-1}Speed=timedistance​=31​15​=15×3=45km h−1 So, speed of car = 45 km h-1.(ii) distance = 15 km1 km = 1000 m15 km = 15 x 1000 = 15000 mtime = 20 min1 min = 60 sec20 min = 20 x 60 = 1200 secSpeed=distancetime=150001200=12.5 m s−1\text{Speed} = \dfrac{\text{distance}}{\text{time}} \[1em] = \dfrac{\text{15000}}{\text{1200}} = 12.5 \text{ m s}^{-1}Speed=timedistance​=120015000​=12.5 m s−1So, speed of car = 12.5 m s-1.

Question 11

Question 15How long a train will take to travel a distance of 200 km with a speed of 60 km h-1?

Accepted Answer

distance = 200 km; speed = 60 km h-1time = ?Speed=distancetime60=200timetime=20060=3h 20min\text{Speed} = \dfrac{\text{distance}}{\text{time}} \[1em] \text{60} = \dfrac{\text{200}}{\text{time}} \[1em] \text{time} = \dfrac{\text{200}}{\text{60}} = 3\text{h } 20\text{min}Speed=timedistance​60=time200​time=60200​=3h 20minSo, time taken by train will be 3 hrs 20 minutes.

Question 12

Question 16A boy travels with a speed of 10 m s-1 for 30 minute. How much distance does he travel?

Accepted Answer

Speed = 10 m s-1time = 30 minutes1 min = 60 sec30 min = 60 x 30 = 1800 secdistance = ?Speed=distancetime10=distance1800distance=1800×10=18000 m\text{Speed} = \dfrac{\text{distance}}{\text{time}} \[1em] \text{10} = \dfrac{\text{distance}}{\text{1800}} \[1em] \text{distance} = 1800 \times 10 = 18000 \text{ m}Speed=timedistance​10=1800distance​distance=1800×10=18000 mSo, distance travelled = 18000 m or 18 km.

Question 13

Question 18Express 15 m s-1 in km h-1.

Accepted Answer

1 m s-1 = 3.6 km h-115 m s-1 = 3.6 x 15 = 54 km h-1So, 15 m s-1 = 54 km h-1.

Question 14

Question 1Write true or false for each statement:(a) The S.I. unit of volume is litre.(b) A measuring beaker of capacity 200 mL can measure only the volume of 200 mL of a liquid.(c) cm2 is a smaller unit of area than m2.(d) Equal volumes of two different substances have equal masses.(e) The S.I. unit of density is g cm-3.(f) 1 g cm-3 = 1000 kg m-3.(g) The density of water is maximum at 4°C.(h) The speed 5 m s-1 is less than 25 km h-1.(i) The S.I. unit of speed is m s-1.

Accepted Answer

(a) FalseCorrect Statement — The S.I. unit of volume is cubic metre (m3).(b) True(c) True(d) FalseCorrect Statement — Equal volumes of two different substances have different masses.(e) FalseCorrect Statement — The S.I. unit of density is kg m-3.(f) True(g) True(h) True(i) True

Question 15

Question 3State two smaller units of volume. How are they related to the S.I. unit?

Accepted Answer

The two smaller units of volume are cubic centimetre (cm3), cubic decimetre (dm3).1 m3 = 1 m x 1 m x 1 m= 100 cm x 100 cm x 100 cm= 1000000 cm3= 106 cm3So, 1 m3 = 106 cm31 m3 = 1 m x 1 m x 1 m= 10 dm x 10 dm x 10 dm= 1000 dm3= 103 dm3So, 1 m3 = 103 dm3

Question 16

Question 5Name two devices which are used to measure the volume of an object. Draw their neat diagrams.

Accepted Answer

The two devices which are used to measure the volume of an object are:Measuring cylinderMeasuring beaker

Question 17

Question 13How does the density of water change when:(a) it is heated from 0°C to 4°C,(b) it is heated from 4°C to 10°C ?

Accepted Answer

(a) Water when heated from 0°C to 4°C, it contracts so density of water increases and becomes maximum at 4°C.(b) When water is heated from 4°C to 10°C it expands, so density decreases.

Question 18

Question 17A car travels with a speed 12 m s-1, while a scooter travels with a speed 36 km h-1. Which of the two travels faster?

Accepted Answer

Speed of car = 12 m s-1Speed of scooter = 36 km h-11 km h-1 = 518\dfrac{	ext{5}}{	ext{18}}185​ m s-136 km h-1 = 36 x 518\dfrac{	ext{5}}{	ext{18}}185​ = 10 m s-1So speed of scooter = 10 m s-1So car travels faster than scooter; since speed of car is more than that of scooter.

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