Work, Energy & Power
Q. A roller coaster at the top of a hill has a height of 30 m. If it has a mass of 500 kg, what is its potential energy at the top?
A.
1500 J
B.
3000 J
C.
7500 J
D.
15000 J
Show solution
Solution
Potential energy = mgh = 500 * 9.8 * 30 = 147000 J.
Correct Answer: D — 15000 J
Learn More →
Q. A roller coaster at the top of a hill has a height of 30 m. If it has a mass of 500 kg, what is its potential energy? (g = 9.8 m/s²)
A.
14700 J
B.
9800 J
C.
15000 J
D.
5000 J
Show solution
Solution
Potential energy is given by PE = mgh. Here, PE = 500 * 9.8 * 30 = 14700 J.
Correct Answer: A — 14700 J
Learn More →
Q. A roller coaster at the top of a hill has a potential energy of 5000 J. If it descends to a height of 10 m, what is its speed at the bottom? (g = 9.8 m/s²)
A.
10 m/s
B.
20 m/s
C.
30 m/s
D.
40 m/s
Show solution
Solution
Using conservation of energy, initial PE + KE = final PE + KE. 5000 J = mgh + 0.5mv². Solving gives v = √(2(5000 - mgh)/m) = 30 m/s.
Correct Answer: C — 30 m/s
Learn More →
Q. A roller coaster starts from rest at a height of 30 m. What is its speed at the lowest point? (g = 9.8 m/s²)
A.
10 m/s
B.
15 m/s
C.
20 m/s
D.
25 m/s
Show solution
Solution
Using conservation of energy, potential energy at the top = kinetic energy at the bottom. mgh = 0.5mv². Solving gives v = √(2gh) = √(2 * 9.8 * 30) = 24.5 m/s.
Correct Answer: C — 20 m/s
Learn More →
Q. A roller coaster starts from rest at a height of 50 m. What is its speed at the lowest point? (g = 9.8 m/s²)
A.
10 m/s
B.
20 m/s
C.
30 m/s
D.
40 m/s
Show solution
Solution
Using conservation of energy, mgh = 0.5mv². Thus, v = sqrt(2gh) = sqrt(2 * 9.8 * 50) = 31.3 m/s, approximately 30 m/s.
Correct Answer: C — 30 m/s
Learn More →
Q. A roller coaster starts from rest at a height of 50 m. What is its speed at the lowest point?
A.
10 m/s
B.
20 m/s
C.
30 m/s
D.
40 m/s
Show solution
Solution
Using conservation of energy, potential energy at the top = kinetic energy at the bottom. mgh = 0.5mv^2. Solving gives v = sqrt(2gh) = sqrt(2*9.8*50) = 31.3 m/s.
Correct Answer: C — 30 m/s
Learn More →
Q. A spring with a spring constant of 200 N/m is compressed by 0.1 m. What is the potential energy stored in the spring?
A.
1 J
B.
2 J
C.
3 J
D.
4 J
Show solution
Solution
Potential Energy = 0.5 × k × x² = 0.5 × 200 N/m × (0.1 m)² = 1 J.
Correct Answer: A — 1 J
Learn More →
Q. A spring with a spring constant of 200 N/m is compressed by 0.1 m. What is the work done in compressing the spring?
A.
1 J
B.
2 J
C.
3 J
D.
4 J
Show solution
Solution
Work done = 0.5 × k × x^2 = 0.5 × 200 N/m × (0.1 m)^2 = 1 J.
Correct Answer: A — 1 J
Learn More →
Q. A spring with a spring constant of 200 N/m is compressed by 0.5 m. What is the potential energy stored in the spring?
A.
25 J
B.
50 J
C.
100 J
D.
200 J
Show solution
Solution
Potential Energy in spring = 0.5 × k × x² = 0.5 × 200 N/m × (0.5 m)² = 25 J.
Correct Answer: B — 50 J
Learn More →
Q. A spring with a spring constant of 200 N/m is compressed by 0.5 m. What is the work done in compressing the spring?
A.
25 J
B.
50 J
C.
100 J
D.
200 J
Show solution
Solution
Work done = 0.5 × k × x² = 0.5 × 200 N/m × (0.5 m)² = 25 J.
Correct Answer: B — 50 J
Learn More →
Q. An object is lifted to a height of 10 m. If the mass of the object is 5 kg, what is the gravitational potential energy gained?
A.
50 J
B.
100 J
C.
150 J
D.
200 J
Show solution
Solution
Potential Energy = mass × g × height = 5 kg × 9.8 m/s² × 10 m = 490 J.
Correct Answer: B — 100 J
Learn More →
Q. An object is lifted vertically 10 m against gravity. If the mass of the object is 5 kg, what is the work done against gravity?
A.
50 J
B.
100 J
C.
150 J
D.
200 J
Show solution
Solution
Work done = mass × g × height = 5 kg × 9.8 m/s² × 10 m = 490 J.
Correct Answer: B — 100 J
Learn More →
Q. An object is lifted vertically 3 m against gravity. If the mass of the object is 4 kg, what is the work done against gravity? (g = 9.8 m/s²)
A.
117.6 J
B.
39.2 J
C.
29.4 J
D.
19.6 J
Show solution
Solution
Work done = mgh = 4 kg × 9.8 m/s² × 3 m = 117.6 J.
Correct Answer: A — 117.6 J
Learn More →
Q. An object is lifted vertically to a height of 10 m. If the mass of the object is 5 kg, what is the work done against gravity?
A.
50 J
B.
100 J
C.
150 J
D.
200 J
Show solution
Solution
Work done = mass × g × height = 5 kg × 9.8 m/s² × 10 m = 490 J.
Correct Answer: B — 100 J
Learn More →
Q. An object is moving in a circular path with a constant speed. What can be said about the work done by the centripetal force?
A.
Positive work
B.
Negative work
C.
Zero work
D.
Depends on speed
Show solution
Solution
Centripetal force does no work as it acts perpendicular to the direction of motion.
Correct Answer: C — Zero work
Learn More →
Q. An object is moving in a circular path with a constant speed. What type of energy is primarily involved?
A.
Kinetic Energy
B.
Potential Energy
C.
Mechanical Energy
D.
Thermal Energy
Show solution
Solution
The object has Kinetic Energy due to its motion in the circular path.
Correct Answer: A — Kinetic Energy
Learn More →
Q. An object is thrown vertically upwards with a speed of 15 m/s. What is the maximum height it reaches? (g = 10 m/s²)
A.
11.25 m
B.
22.5 m
C.
15 m
D.
20 m
Show solution
Solution
Maximum Height (h) = v^2 / (2g) = (15^2) / (2 * 10) = 11.25 m
Correct Answer: B — 22.5 m
Learn More →
Q. If 10^(2x) = 100, what is the value of x?
Show solution
Solution
100 = 10^2, so 2x = 2, hence x = 1.
Correct Answer: B — 0.5
Learn More →
Q. If 10^x = 0.01, what is the value of x?
Show solution
Solution
Since 0.01 = 10^(-2), we have x = -2.
Correct Answer: A — -2
Learn More →
Q. If 2^(x+1) = 16, what is the value of x?
Show solution
Solution
16 = 2^4 => x + 1 = 4 => x = 3
Correct Answer: B — 3
Learn More →
Q. If 3^(2x) = 81, what is the value of x?
Show solution
Solution
Since 81 = 3^4, we have 3^(2x) = 3^4, thus 2x = 4, giving x = 2.
Correct Answer: A — 2
Learn More →
Q. If 4^x = 64, what is the value of x?
Show solution
Solution
Since 64 = 4^3, we have x = 3.
Correct Answer: B — 3
Learn More →
Q. If 5^(x+1) = 125, what is the value of x?
Show solution
Solution
125 = 5^3, so x + 1 = 3, hence x = 2.
Correct Answer: B — 2
Learn More →
Q. If 5^(x-1) = 25, what is the value of x?
Show solution
Solution
Since 25 = 5^2, we have 5^(x-1) = 5^2, thus x - 1 = 2, giving x = 3.
Correct Answer: A — 2
Learn More →
Q. If 5^x = 125, what is the value of x?
Show solution
Solution
125 = 5^3 => x = 3
Correct Answer: C — 3
Learn More →
Q. If 5^x = 25, what is the value of x?
Show solution
Solution
Since 25 = 5^2, we have 5^x = 5^2, thus x = 2.
Correct Answer: B — 2
Learn More →
Q. If 7^(x) = 49, what is the value of x?
Show solution
Solution
49 = 7^2, so x = 2.
Correct Answer: B — 2
Learn More →
Q. If 8^(x) = 64, what is the value of x?
Show solution
Solution
64 = 8^2, so x = 2.
Correct Answer: B — 2
Learn More →
Q. If a 10 kg object is dropped from a height of 20 m, what is its potential energy at the top? (1960)
A.
200 J
B.
1000 J
C.
500 J
D.
1500 J
Show solution
Solution
Potential Energy (PE) = m * g * h = 10 kg * 9.8 m/s^2 * 20 m = 1960 J
Correct Answer: B — 1000 J
Learn More →
Q. If a 10 kg object is dropped from a height of 5 m, what is the potential energy at that height?
A.
50 J
B.
100 J
C.
150 J
D.
200 J
Show solution
Solution
Potential energy = mgh = 10 kg × 9.8 m/s² × 5 m = 490 J.
Correct Answer: B — 100 J
Learn More →
Showing 151 to 180 of 252 (9 Pages)
