Q. A retailer sells a bicycle for $300 after applying a discount of 10%. What was the original price of the bicycle?
A.$270
B.$330
C.$300
D.$350
Solution
Let the original price be x. After a 10% discount, the selling price is x - (0.10 * x) = 0.90x. Setting this equal to $300 gives 0.90x = $300, so x = $300 / 0.90 = $333.33.
Q. A rigid body is rotating about a fixed axis with an angular velocity ω. If the moment of inertia of the body is I, what is the angular momentum of the body?
A.Iω
B.ω/I
C.I/ω
D.Iω^2
Solution
Angular momentum L = Iω, where I is the moment of inertia and ω is the angular velocity.
Q. A rigid body is rotating about a fixed axis. If the moment of inertia of the body is I and it is rotating with an angular velocity ω, what is its angular momentum?
A.Iω
B.I/ω
C.Iω^2
D.ω/I
Solution
Angular momentum L = Iω, where I is the moment of inertia and ω is the angular velocity.
Q. A rigid body rotates about a fixed axis with an angular velocity ω. If the moment of inertia of the body is I, what is the angular momentum of the body?
A.Iω
B.ω/I
C.I/ω
D.Iω^2
Solution
Angular momentum L = Iω, where I is the moment of inertia and ω is the angular velocity.
Q. A river basin has an area of 200 km². If the average rainfall is 1000 mm per year, what is the total volume of water received by the basin in a year?
A.200 million m³
B.100 million m³
C.300 million m³
D.400 million m³
Solution
Volume = Area × Rainfall = 200 km² × 1000 mm = 200 km² × 1 m = 200 million m³.
Q. A river basin has an area of 200 square kilometers. If the average rainfall is 800 mm per year, how much water (in cubic meters) falls on the basin annually? (2019)
A.160000000 m³
B.200000000 m³
C.240000000 m³
D.320000000 m³
Solution
Water volume = Area × Rainfall = 200 km² × 800 mm = 200000000 m³.
Q. A river basin has an area of 500 km². If the average rainfall is 800 mm per year, what is the total volume of water received by the basin in a year? (2019)
A.400,000,000 m³
B.500,000,000 m³
C.600,000,000 m³
D.700,000,000 m³
Solution
Volume = area × rainfall = 500 km² × 800 mm = 500,000,000 m³.
Q. A river flows through a region with a soil erosion rate of 5 tons per hectare per year. If the area of the watershed is 100 hectares, how much soil is eroded in a year?
Q. A river flows through a region with a soil retention capacity of 20% of its volume. If the river has a volume of 1000 m³, how much water can be retained by the soil? (2023)
A.100 m³
B.200 m³
C.300 m³
D.400 m³
Solution
Water retained = 20% of 1000 m³ = 0.2 × 1000 m³ = 200 m³.
Q. A river flows through a valley with a gradient of 1 in 1000. If the river descends 2 meters over a distance of 2000 meters, is the gradient consistent? (2023)
A.Yes
B.No
C.Not enough information
D.Depends on the soil type
Solution
Gradient = Rise / Run = 2 m / 2000 m = 1 in 1000, so it is consistent.
Q. A river flows through a valley with a gradient of 1:1000. If the river descends 2 meters over a distance of 2000 meters, is the gradient consistent? (2022)
A.Yes
B.No
C.Not enough information
D.Depends on the soil type
Solution
Gradient = Rise / Run = 2 m / 2000 m = 1:1000, so it is consistent.
Q. A river has a length of 150 km and a width of 50 m. If the average depth is 3 m, what is the approximate volume of water in the river in cubic meters?
A.22500000
B.2250000
C.15000000
D.30000000
Solution
Volume = Length × Width × Depth = 150000 m × 50 m × 3 m = 22500000 m³.
Q. A river has a width of 300 meters and a depth of 5 meters. What is the volume of water flowing through the river in one second if the flow speed is 2 m/s? (2020)
A.3000 m³/s
B.6000 m³/s
C.1500 m³/s
D.1200 m³/s
Solution
Volume = Width × Depth × Speed = 300 m × 5 m × 2 m/s = 3000 m³/s.
