This question is concerned with the effects of acceleration on a direct reading magnetic compass. These effects depend upon the magnetic latitude, the direction of flight and the acceleration rate.
The lines of force produced by the earths magnetic field flow vertically upwards, out of the ground at the magnetic south pole and vertically into the ground at the magnetic north pole. The degree to which they are inclined vertically at all other points on the earth is determined by the magnetic latitude. At the magnetic equator they are horizontal or parallel with the surface. As magnetic latitudes increase towards the magnetic poles the degree of inclination also increases. The inclination of the lines of force causes the magnets in compasses to dip below the horizontal, thereby reducing their accuracy.
In order to minimise this problem, compasses are typically suspended such that their C of G is lower than their pivot. In this way the weight of the magnet is made to oppose the dipping caused by the lines of magnetic force. This is termed pendulous suspension. Although this reduces compass dip, it does not entirely eliminate it. This means that the C of G of the compass magnet will be off-set to one side of the pivot such that the C of G moves away from the nearest pole. This means that the suspension point is between the nearest pole and the C of G of the magnet.
Whenever an aircraft accelerates or decelerates on heading other than due north or due south, the lateral displacement of the C of G and the inertia its compass magnet, causes the magnet to rotate. The magnitude and direction of this rotation is determined by the aircraft heading, the hemisphere and the acceleration or deceleration rate.
This question specifies acceleration on a westerly heading in the northern hemisphere. This will cause the compass magnet to rotate anti-clockwise. The compass magnet is fixed to the compass card, so the compass indication will increase. This will indicate a turn to the north. This answer illustrates the more general result that accelerations cause an apparent turn towards the nearest pole. Decelerations will have the opposite effect, producing an apparent turn away from the nearest pole.