# Measurements of Length, Mass, Density, and Time

Measurement of time:

**Period**: time taken for 1 complete oscillation**frequency**: number of complete oscillations per secondthe period increases with the length of the pendulum

## MCQ Questions

1. 0.05km written in the standard form is

a. 5/100 km

b. 0.5 x 10^{-1}km

c. 5 x 10^{-2}km

d. 40 x 10^{-3}km

2. To measure length using a metre rule, wrong positioning of the eye leads to

a. parallax error

b. eye error

c. zero error

d. metre error

3. Which of the following instruments is most suitable for measuring the internal diameter of a 100ml beaker?

a. metre rule

b. vernier calipers

c. measuring tape

d. external calipers

4. The mass of an object is reduced if its

a. state is changed

b. amount of matter is decreased

c. surface area is decreased

d. volume is increased

5. A cuboid with length 3cm, width 4cm and height 10cm is made from wood of density 0.5gcm^{-3}. The mass of the cuboid is

a. 17.5g

60g

120g

240g

6. It is easier to float in the sea than in a swimming pool because

a. the seawater is denser than the water in the pool

b. the seawater is less dense than the water in the pool

c. the seawater is warmer than the water in the pool

d. the seawater is cooler than the water in the pool

7. To correct a fast-running pendulum clock,

a. decrease the length of the pendulum

b. increase the length of the pendulum

c. increase the mass of the pendulum bob

d. decrease the mass of the pendulum

8. A ticker-tape timer vibrates 10 times a second. What is the time interval between two consecutive dots?

a. 0.1s

b. 1s

c. 2s

d. 10s

9. The bob of a simple pendulum takes 18.8s to swing from P to Q and back to P again twenty times. What is the period of the pendulum?

a. 0.47s

b 0.94s

c. 1.88s

d. 3.96s

10. A box weighs 100N on Earth. Given that the acceleration due to gravity is 10ms^{-2} on Earth and the acceleration due to gravity is 4ms^{-2} on Mars, what is the mass and weight of the box on Mars?

Mass Weight

a. 10kg 100N

b. 10kg 40N

c. 25kg 100N

d. 25kg 40N

11. Which of the following experiences the same gravitational field strength?

(1) A 50kg mass resting on the floor

(2) A 50kg mass hanging on a 20m tall tree

(3) A 50kg mass dropping from a 20m tall tree

(4) A 100kg mass resting on the floor

a. (1) and (2) only

b. (1), (2) and (3) only

c. (1), (2) and (4) only

d. All of the above

12. Which of the following statement(s) is/are always true?

(1) The inertia of an object is dependent on the size of the object

(2) Metal is heavier than feather

(3) When the mass of an object increases, the weight of the object will also increase

a. (3) only

b. (1) and (3)

c. All of the above

d. none of the above

### MCQ Answers

1. c

2. a

3. b

4. b

5. b

6. a

7. b

8. a

9. b

10. b

11. d (The gravitational field strength (g) has a constant value of 10N/kg when acting on any object near to Earth's surface. g changes when there is a big change in the mass of the earth or when the object goes deep underground or very high above the earth's surface. The mass of the object and the small distance of 20m from the earth's surface do not cause the object to experience different g)

12. d (The inertia of an object depends on the mass and not the size. Metal is denser than feather but not necessarily heavier than feather. In space where there is zero gravity, when the mass of an object increases, the weight remains at 0)

## Structured Question Worked Solutions

**1. What is the reading on the vernier calipers?**

**Solution**

5.47cm

**2. What is the reading on the micrometer screw gauge?**

**Solution**

6.5mm+0.18mm=6.68mm

**3. The mass of 600 spherical lead pellets is found to be 66g and the total volume of the pellets is found to be 5.7cm**^{3}**. Calculate**

**a. the total weight of the pellets**

**b. the volume of one pellet**

**(the force of gravity acting on a mass of 1.00kg is 10.0N)**

**Solution**

a. 0.66N

b. 0.0095cm^{3}

**4a. What is meant by the period of a simple pendulum?**

**b. The period of a simple pendulum 1m long is about 2s. State clearly how you would determine the period of such a pendulum as accurately as possible, using a stopclock accurate to within 0.1s.**

**Solution**

a. Period is the time taken for a pendulum to swing one complete oscillation.

b. Set a simple pendulum to oscillate, ensuring that the angular displacement does not exceed 5°. Ignoring the first few oscillations,, time only the steady oscillations. Obtain the time for 20 oscillations, and divide this time by 20 to calculate the period. For better accuracy, the experiment can be repeated a few times to obtain the average value of the period.

**5. When a block of metal is hung in air from a spring balance, the reading is 9.6N.**

**a. What is the weight of the block of metal?**

**b. Assuming that the weight of a 1kg mass is 10N, what is the mass of the block of metal?**

**Solution**

a. 9.6N

b. 0.96kg

**6. A rectangular block measures length 1.00cm, width 2.50cm, and height 4.00cm.**

**a. Name the instrument used to measure the sides of the rectangular block**

**b. Calculate the volume of the rectangular block**

**c. If the mass of the rectangular block is 300g, find the density of the block**

**Solution**

a. vernier calipers

b. 10cm^{3}

c. 30gcm^{‐3}

**7. State one advantage and one disadvantage of using the micrometer screw gauge for measuring length.**

**Solution**

advantage: high accuracy, accurate to 0.01mm

disadvantage: has a short range usually between 0 to 25mm

**8. State 4 advantages of using the measuring tape as an instrument for measuring lengths.**

**Solution**

can be very long

can be used to measure bent lines

can be used to measure circumference

portable

**9. The internal and external radius of a hollow silver sphere are 7cm and 14cm respectively. Find the mass of the sphere, given that the density of silver is 10 500 kgm**^{-3}

**Solution**

**10. Explain why the density of gas is usually stated together with its temperature.**

**Solution**

Density is the mass per unit volume. As the volume of gas changes with temperature, the density also changes with temperature. Hence, the density of gas is usually stated with its temperature.