*Question*

**(a)Mass, length and time are SІ base quantities.State two other base quantities.1. …………………………………………………………………………………………………………………………….2. …………………………………………………………………………………………………………………………….**

(b) A mass m is placed on the end of a spring that is hanging vertically, as shown in Fig. 1.1.

The mass is made to oscillate vertically. The time period of the oscillations of the mass is T.

The period T is given by

\(T = C\sqrt{\frac{m}{k}}\)

where C is a constant and k is the spring constant.

Show that C has no units.

**Answer/Explanation**

(a)

temperature

current

(allow amount of substance and luminous intensity)

(b)

base units of force constant: kgms^{–2} m^{–1} or kg s^{–2}

base units of time and mass: s and kg

base units of C: s (kgs^{–2} / kg)^{1/2} cancelling to show no units

### Question

**(a) Distinguish between mass and weight.****mass: ……………………………………………………………………………………………………………….****…………………………………………………………………………………………………………………………****weight: ………………………………………………………………………………………………………………****…………………………………………………………………………………………………………………………[2]**

(b) An object O of mass 4.9 kg is suspended by a rope A that is fixed at point P. The object is pulled to one side and held in equilibrium by a second rope B, as shown in Fig. 2.1.

Rope A is at an angle θ to the horizontal and rope B is horizontal. The tension in rope A is 69 N and the tension in rope B is T.

(i) On Fig. 2.1, draw arrows to represent the directions of all the forces acting on object O. [2]

(ii) Calculate

1. the angle θ,

θ = …………………………………………° [3]

2. the tension T.

T = ………………………………………. N [2]

**Answer/Explanation**

Ans:

**(a)** mass is the property of a body resisting changes in motion / quantity of matter in a body / measure of inertia to changes in motion

weight is the force due to the gravitational field/force due to gravity or gravitational force Allow 1/2 for ‘mass is scalar weight is vector’

**(b)(i)** arrow vertically down through O tension forces in correct direction on rope.