Physics 2009 Jamb Examination

Power is the rate of doing work. The work done in lifting an object vertically is given by the product of its weight and height.\[ \text{Work done} = mgh \]Substituting values:\[ = 750 \times 10 \times 90 = 675000 \; \text{J} \]The time taken is 1 minute = 60 s.
Therefore, power is:\[ P = \dfrac{\text{Work done}}{\text{Time}} = \dfrac{675000}{60} = 11250 \; \text{W} \]\[ P = 11.25 \; \text{kW} \]This shows the total power expended while lifting the load is 11.25 kW.

For equilibrium on a rough surface, the limiting frictional force equals the applied force when motion is impending.\[ F = \mu R \]Where \( R = mg \) is the normal reaction.
Thus,\[ 500 = \mu (80 \times 10) \]\[ 500 = 800\mu \]\[ \mu = \dfrac{500}{800} = 0.625 \]Therefore, the coefficient of static friction is approximately 0.6.

For an inclined plane, the velocity ratio \( VR = \dfrac{1}{\sin \theta} \).
Given \( \theta = 30° \):\[ VR = \dfrac{1}{\sin 30°} = \dfrac{1}{0.5} = 2 \]Hence, the velocity ratio for a 30° incline is 2.

The pressure at a point in a fluid is given by \( P = h\rho g \), where \( h \) is the depth, \( \rho \) is the density, and \( g \) is acceleration due to gravity.
Pressure depends only on these three factors and not on the shape of the container or the constituents of the liquid, provided the density remains constant.
Therefore, the type of container (III) and constituents of the liquid (IV) do not affect the pressure.

The work done in stretching a spring or elastic cord is given by:\[ W = \dfrac{1}{2} F x \]Given:
\( F = 10 \; \text{N} \), \( x = 1.2 \; \text{cm} = 0.012 \; \text{m} \)\[ W = \dfrac{1}{2} \times 10 \times 0.012 = 0.06 \; \text{J} \]\[ W = 6.0 \times 10^{-2} \; \text{J} \]Thus, the total work done is 6.0 × 10⁻² J.

A micrometer screw gauge is designed to measure very small dimensions with high precision such as the diameter of small spherical objects or thin materials.
It is suitable for measuring the diameter of small ball bearings and the thickness of paper.
It cannot be used for larger measurements like cylinder diameters or wire lengths which require a vernier caliper or metre rule respectively.

Acceleration is the rate of change of velocity with time.\[ a = \dfrac{v_2 - v_1}{t_2 - t_1} \]Substituting values:\[ a = \dfrac{35 - 15}{20 - 10} = \dfrac{20}{10} = 2 \; \text{m/s}^2 \] Hence, the acceleration between the two points is 2.00 m/s².

At maximum height, the final velocity \( v = 0 \).
Using the equation of motion:\[ v = u - gt \]\[ 0 = u - 10 \times 4 \Rightarrow u = 40 \; \text{m/s} \]The bullet was fired with an initial velocity of 40 m/s to reach its maximum height in 4 seconds.

Simple harmonic motion (SHM) occurs when an object moves about a mean position under a restoring force proportional to its displacement and directed towards that position.
The oscillation of a loaded test tube vertically and the motion of pistons in an engine are examples of approximate SHM. The beating of the heart also exhibits rhythmic periodic motion akin to SHM.
Therefore, motions II, III, and V exhibit simple harmonic behaviour.

The energy required to boil off the water is given by:\[ Q = mL \]Where \( m = 2 \; \text{kg} \), \( L = 2.3 \times 10^6 \; \text{J/kg} \).\[ Q = 2 \times 2.3 \times 10^6 = 4.6 \times 10^6 \; \text{J} \]Power is defined as energy per unit time:\[ P = \dfrac{Q}{t} \Rightarrow t = \dfrac{Q}{P} \]Substituting \( P = 1000 \; \text{W} \):\[ t = \dfrac{4.6 \times 10^6}{1000} = 4.6 \times 10^3 \; \text{s} \]Therefore, it takes 4.6 × 10³ seconds to completely boil off the water.