For small angles, T ≈ 2π√(L/g). Assuming L = 1 m, T ≈ 2π√(1/9.8) ≈ 2.0 s.

The period T of a simple pendulum is given by T = 2π√(L/g). If L is doubled, T becomes T' = 2π√(2L/g) = √2 * T = 1.41 s.

The period T = 2π√(L/g). If L is increased by a factor of 4, T increases by a factor of √4 = 2.

The period of a pendulum is given by T = 2π√(L/g). If L is increased to 4L, T becomes 2π√(4L/g) = 2T = 2 seconds.

The period T = 2π√(L/g). If L is tripled, T becomes √3 times longer, so T = 2 s.

Length L = (gT^2)/(4π^2) = (9.8 * 1^2)/(4 * π^2) ≈ 1 m.

Angular frequency (ω) = 2π/T = 2π/1.5 = 4π/3 rad/s.

Frequency (f) is the reciprocal of the period (T). Therefore, f = 1/T = 1/2 = 0.5 Hz.

The period T of a simple pendulum is given by T = 2π√(L/g). Rearranging gives L = (T²g)/(4π²). Using g = 9.8 m/s², L = (2² * 9.8)/(4π²) ≈ 1 m.

Using the formula T = 2π√(l/g), we have l = (T² * g)/(4π²) = (2² * 10)/(4π²) = 1 m.

The period T of a simple pendulum is given by T = 2π√(L/g). For length 4L, T' = 2π√(4L/g) = 2T.

In simple harmonic motion, the restoring force is proportional to the displacement from the equilibrium position.

A pendulum swinging with a small amplitude exhibits simple harmonic motion.

Percentage uncertainty = (Uncertainty / Measured value) * 100 = (0.1 / 2.0) * 100 = 5%.

Relative uncertainty = (Uncertainty / Measured value) * 100 = (0.1 / 2.0) * 100 = 5%.

Fractional error = (absolute error / measured value) = 0.1 / 2.0 = 0.05.

Cost of 3 pens = 3 × 2 = 6. Let the cost of each notebook be x. Then 6 + 2x = 15, leading to 2x = 9, so x = 4.

Profit = Selling Price - Cost Price = $150 - $120 = $30. Percentage profit = (Profit / Cost Price) × 100 = (30/120) × 100 = 25%.

Profit = selling price - cost price = 960 - 800 = 160. Percentage profit = (profit/cost price) * 100 = (160/800) * 100 = 20%.

Loss = Cost Price - Selling Price = 150 - 120 = 30. Loss Percentage = (Loss/Cost Price) * 100 = (30/150) * 100 = 20%.

Profit = Selling price - Cost price = 50 - 40 = 10. Percentage profit = (Profit/Cost price) * 100 = (10/40) * 100 = 25%.

Profit = Selling Price - Cost Price = 50 - 40 = 10. Percentage Profit = (Profit / Cost Price) * 100 = (10/40) * 100 = 25%.

Profit = Selling Price - Cost Price = 600 - 500 = 100. Percentage profit = (Profit / Cost Price) * 100 = (100/500) * 100 = 20%.

Profit = Selling Price - Cost Price = 600 - 500 = 100. Profit Percentage = (Profit/Cost Price) * 100 = (100/500) * 100 = 20%.

Profit = Selling Price - Cost Price = 960 - 800 = 160. Percentage profit = (Profit/Cost Price) * 100 = (160/800) * 100 = 20%.

Speed upstream = Speed in still water - Speed of current = 5 - 2 = 3 km/h.

Distance = Speed × Time = 12 km/h × 1.5 hours = 18 km.

Average speed = Total distance / Total time = 150 km / 2.5 hours = 60 km/h.

Time = Distance / Speed = 180 km / 90 km/h = 2 hours.

Interest = Principal × Rate × Time = 1000 × 0.05 × 3 = $150.