Final answer:
The unknown mass in terms of m is 0.25m when 25% of the energy is transmitted.
Step-by-step explanation:
In order for 25% of the energy to be transmitted when a mass of mass m is slid into a mass of unknown quantity, we can use the equation for energy transmitted:
Etransmitted = η * Einitial
where Etransmitted is the transmitted energy, Einitial is the initial energy, and η is the coefficient of energy transmission. Since we are given that 25% of the energy is transmitted, the coefficient of energy transmission η = 0.25.
Plugging in these values and solving for the unknown mass:
η * Einitial = 0.25 * Einitial = Etransmitted
Therefore, the unknown mass in terms of m is 0.25m.