(a) Two point masses are separated by a distance $x$ in a vacuum. State an expression for the force $F$ between the two masses $M$ and $m$. State the name of any other symbol used. (b) A small sphere S is attached to one end of a rod, as shown in Fig. 1.1. The rod hangs from a vertical thread and is horizontal. The distance from the centre of sphere S to the thread is $8.0\text{ cm}$. A large sphere L is placed near to sphere S, as shown in Fig. 1.2. There is a force of…

Physics 9702/42 — May/June 2019

Cambridge A-Level · A Level Structured Questions · worked solutions for every part, with the mark scheme

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Topics Motion in a Circle · Quantum Physics · Electronics · Magnetic Fields · Gravitational Fields · Thermodynamics · +6 more

Q1Gravitational FieldsMotion in a CircleFree sample

(a)

Two point masses are separated by a distance $x$ in a vacuum.
State an expression for the force $F$ between the two masses $M$ and $m$ .
State the name of any other symbol used.

(b)

A small sphere S is attached to one end of a rod, as shown in Fig. 1.1.

Fig. 1.1

The rod hangs from a vertical thread and is horizontal.
The distance from the centre of sphere S to the thread is $8.0\text{ cm}$ .

A large sphere L is placed near to sphere S, as shown in Fig. 1.2.

Fig. 1.2

There is a force of attraction between spheres S and L, causing sphere S to move through a distance of $1.2\text{ mm}$ .
The line joining the centres of S and L is normal to the rod.

(i)

Show that the angle $\theta$ through which the rod rotates is $1.5 \times 10^{-2}\text{ rad}$ .

(ii)

The rotation of the rod causes the thread to twist.
The torque $T$ (in $\text{N m}$ ) required to twist the thread through an angle $\beta$ (in $\text{rad}$ ) is given by

T = 9.3 \times 10^{-10} \times \beta

Calculate the torque in the thread when sphere L is positioned as shown in Fig. 1.2.

torque = ______ $\text{N m}$

(c)

The distance between the centres of spheres S and L is $6.0\text{ cm}$ .
The mass of sphere S is $7.5\text{ g}$ and the mass of sphere L is $1.3\text{ kg}$ .

(i)

By equating the torque in (b)(ii) to the moment about the thread produced by gravitational attraction between the spheres, calculate a value for the gravitational constant.

gravitational constant = ______ $\text{N m}^2\text{ kg}^{-2}$

(ii)

Suggest why the total force between the spheres may not be equal to the force calculated using Newton’s law of gravitation.

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