Clarification:
Let T signify the pendulum's period. The time's SI unit is seconds (s).
It is influenced by the length of the pendulum, l, and the gravitational acceleration, g.
The SI units for gravitational acceleration, g, and pendulum length, l, are m/s² and m, respectively.
Dividing m by m/s² produces s². Taking the square root of s² results in s, which is the SI unit for the pendulum's period.
Thus,

This concludes the solution we sought.
Response: a. The mirrors and eyepiece of a large telescope are designed with spring-loaded components to quickly return to a predetermined position.
Justification:
Adaptive optics refers to a technique employed by various astronomical observatories to compensate in real-time for the atmospheric turbulence that impacts astronomical imaging.
This is executed by integrating advanced deformable mirrors into the telescope's optical pathway, operated by a set of computer-controlled actuators. This allows for obtaining clearer images despite the atmospheric fluctuations that create distortions.
It is crucial to note that this process requires a moderately bright reference star located closely to the object being studied.
However, locating such stars is not always feasible, prompting the use of a strong laser beam directed at the upper atmosphere to create artificial stars.
The amount of work performed by a system at consistent pressure is defined by the following equation:

where
p represents pressure

as the final volume

as the initial volume
Plugging the values given in this case into the formula gives us

Considering that

, the result for the work done becomes
Answer:
the lump descends
Explanation:
The full articulation of the query is
Upon fully submerging a 3 kg lump of material in a certain fluid, the fluid that would have occupied the space now filled by the lump weighs 2 kg. (a) When released, does the lump float up, sink, or remain steady
(a)
= Buoyant force acting upward on the lump
= mass of irregular lump = 3 kg
= mass of fluid displaced = 2 kg
The upward buoyant force on the lump is given by the weight of the displaced fluid, thus
the weight of the irregular lump of material is represented as

Given that the weight of the lump downward exceeds the upward buoyant force, the lump will indeed descend