Explanation

The period of a simple pendulum is: T = 2π√l/g

A second’s pendulum has a period of 2 seconds (it takes 2 seconds for a full swing) and its length is L.

2 = 2π√L/g ⇒ L = g/π²

Now we want a pendulum with period 1 second:

1 = 2π√l1/g ⇒ l1 = g/4π²

Compare with the second’s pendulum:

l1 = L/4

Explanation

Flow of liquid through a needle depends a lot on the needle’s radius. Very small changes make a big difference.

The rule is: pressure needed is inversely proportional to the fourth power of the radius.

Needle 1: radius = 0.15 mm (0.30 mm diameter)

Needle 2: radius = 0.30 mm (0.60 mm diameter)

Compare the pressures:

Pressure ratio = (0.30/0.15)⁴ = 2⁴ = 16

So the nurse must press 16 times harder for the smaller needle to get the same flow.

Explanation

SHM displacement varies sinusoidally with time.

Amplitude ‘a’ represents the maximum displacement from the mean position.

Explanation

The slower motion of a pendulum is due to a longer period, which is related to the weaker gravitational force at higher altitudes

K2, being a very high mountain, has a significantly lower value of acceleration

Due to gravity, cities like Karachi, Murree, or Lahore result in a slower pendulum motion. 

Explanation

As temperature increases, a black body emits more energy at higher frequencies and shorter wavelengths.

This is explained by Wien's displacement law, which states peak wavelength shifts inversely with temperature.

Explanation

Magnetic force acts perpendicular to motion.

Electron moves along the field → no perpendicular component → no force.

Explanation

Radius of orbit is directly proportional to speed.

Double the speed → double the radius → 4 cm.

Explanation

When the airplane’s nose is lifted by a gust, it oscillates around the equilibrium altitude before settling.

The oscillations gradually decrease in amplitude due to air resistance → typical underdamped motion.

Explanation

In a purely inductive AC circuit, V = I ω L.

Rearrange → L = V/(I ω) = 200/10 = 20 H.

Explanation

According to Einstein’s general relativity, both bodies and light rays follow the curved paths called geodesics in curved spacetime.

In the absence of gravity, geodesics reduce to straight lines.