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Q. A block on a spring oscillates with a frequency of 3 Hz. What is the angular frequency of the motion?

A. 3 rad/s
B. 6 rad/s
C. 9 rad/s
D. 12 rad/s

Solution

Angular frequency (ω) = 2πf = 2π(3) = 6 rad/s.

Correct Answer: B — 6 rad/s

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Q. A block on a spring oscillates with a period of 1.5 seconds. If the mass of the block is halved, what will be the new period?

A. 1.5 s
B. 1.22 s
C. 1.73 s
D. 1.0 s

Solution

The period of a mass-spring system is T = 2π√(m/k). Halving the mass does not change the period since it is independent of mass in this case.

Correct Answer: A — 1.5 s

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Q. A block slides down a frictionless incline of angle 30 degrees. If the incline has a coefficient of kinetic friction of 0.2, what is the acceleration of the block?

A. 4.9 m/s²
B. 3.9 m/s²
C. 2.9 m/s²
D. 1.9 m/s²

Solution

Net force = mg sin(30) - μmg cos(30). Acceleration a = (mg sin(30) - μmg cos(30))/m = g(sin(30) - μ cos(30)). Substituting g = 10 m/s² gives a = 10(0.5 - 0.2 * √3/2) = 4.9 m/s².

Correct Answer: B — 3.9 m/s²

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Q. A boat can row at 5 km/h in still water. If it takes 2 hours to row upstream against a current, how far has it traveled?

A. 5 km
B. 10 km
C. 15 km
D. 20 km

Solution

Distance = speed × time. Upstream speed = 5 - current speed. If current speed is 1 km/h, distance = (5 - 1) × 2 = 8 km.

Correct Answer: B — 10 km

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Q. A boat can travel at 10 km/h in still water. If it is moving downstream in a river flowing at 5 km/h, what is the speed of the boat relative to the riverbank?

A. 5 km/h
B. 10 km/h
C. 15 km/h
D. 20 km/h

Solution

Speed downstream = Speed of boat + Speed of river = 10 km/h + 5 km/h = 15 km/h.

Correct Answer: C — 15 km/h

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Q. A boat can travel at 10 km/h in still water. If the current flows at 2 km/h, what is the speed of the boat downstream?

A. 8 km/h
B. 10 km/h
C. 12 km/h
D. 14 km/h

Solution

Speed downstream = speed of boat + speed of current = 10 + 2 = 12 km/h.

Correct Answer: C — 12 km/h

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Q. A boat can travel at 10 km/h in still water. If the current of the river is 2 km/h, what is the speed of the boat downstream?

A. 8 km/h
B. 10 km/h
C. 12 km/h
D. 14 km/h

Solution

Speed downstream = speed of boat + speed of current = 10 + 2 = 12 km/h.

Correct Answer: C — 12 km/h

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Q. A boat can travel at 12 km/h in still water. If it is going downstream in a river flowing at 3 km/h, what is the speed of the boat relative to the riverbank?

A. 9 km/h
B. 12 km/h
C. 15 km/h
D. 3 km/h

Solution

Speed of boat downstream = Speed of boat + Speed of river = 12 km/h + 3 km/h = 15 km/h.

Correct Answer: C — 15 km/h

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Q. A boat can travel at 12 km/h in still water. If it is going downstream in a river flowing at 4 km/h, what is the speed of the boat relative to the riverbank?

A. 8 km/h
B. 12 km/h
C. 16 km/h
D. 20 km/h

Solution

Speed of boat downstream = Speed of boat + Speed of river = 12 km/h + 4 km/h = 16 km/h.

Correct Answer: C — 16 km/h

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Q. A boat can travel at 12 km/h in still water. If it is moving downstream in a river flowing at 4 km/h, what is the speed of the boat relative to the riverbank?

A. 8 km/h
B. 12 km/h
C. 16 km/h
D. 4 km/h

Solution

Speed of boat relative to riverbank = Speed of boat + Speed of river = 12 km/h + 4 km/h = 16 km/h.

Correct Answer: C — 16 km/h

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Q. A boat can travel at 12 km/h in still water. If it travels downstream in a river flowing at 3 km/h, what is its speed relative to the riverbank?

A. 9 km/h
B. 12 km/h
C. 15 km/h
D. 18 km/h

Solution

Speed downstream = Speed of boat + Speed of river = 12 km/h + 3 km/h = 15 km/h.

Correct Answer: C — 15 km/h

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Q. A boat can travel at 15 km/h in still water. If it takes 2 hours to go upstream and 1 hour to return downstream, what is the speed of the current?

A. 3 km/h
B. 4 km/h
C. 5 km/h
D. 6 km/h

Solution

Let speed of current = x. Upstream speed = 15 - x, Downstream speed = 15 + x. Distance = speed × time. 2(15 - x) = 1(15 + x). Solving gives x = 5 km/h.

Correct Answer: C — 5 km/h

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Q. A boat can travel at 15 km/h in still water. If it takes 2 hours to travel upstream and 1.5 hours to travel downstream, what is the speed of the current?

A. 2 km/h
B. 3 km/h
C. 4 km/h
D. 5 km/h

Solution

Let speed of current = x. Upstream speed = 15 - x, Downstream speed = 15 + x. (2 hours)(15 - x) = (1.5 hours)(15 + x). Solving gives x = 3 km/h.

Correct Answer: B — 3 km/h

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Q. A boat can travel at a speed of 10 km/h in still water. If the speed of the current is 2 km/h, what is the speed of the boat downstream?

A. 8 km/h
B. 10 km/h
C. 12 km/h
D. 14 km/h

Solution

Speed downstream = speed of boat + speed of current = 10 + 2 = 12 km/h.

Correct Answer: C — 12 km/h

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Q. A boat is moving upstream at 10 km/h in a river that flows at 5 km/h. What is the speed of the boat relative to the riverbank?

A. 5 km/h
B. 10 km/h
C. 15 km/h
D. 0 km/h

Solution

Speed of boat relative to riverbank = Speed of boat - Speed of river = 10 km/h - 5 km/h = 5 km/h.

Correct Answer: C — 15 km/h

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Q. A boat is moving upstream at 10 km/h in a river that flows downstream at 5 km/h. What is the speed of the boat relative to the ground?

A. 5 km/h
B. 10 km/h
C. 15 km/h
D. 20 km/h

Solution

Speed of boat relative to ground = Speed of boat - Speed of river = 10 km/h - 5 km/h = 5 km/h.

Correct Answer: A — 5 km/h

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Q. A boat is moving upstream at 10 km/h in a river that flows downstream at 5 km/h. What is the speed of the boat relative to the riverbank?

A. 5 km/h
B. 10 km/h
C. 15 km/h
D. 20 km/h

Solution

Speed of boat relative to riverbank = Speed of boat - Speed of river = 10 km/h - 5 km/h = 5 km/h.

Correct Answer: A — 5 km/h

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Q. A boat travels 30 km downstream in 2 hours. What is the speed of the boat in still water if the speed of the current is 5 km/h?

A. 10 km/h
B. 15 km/h
C. 20 km/h
D. 25 km/h

Solution

Speed downstream = distance/time = 30/2 = 15 km/h. Speed of boat in still water = speed downstream - speed of current = 15 - 5 = 10 km/h.

Correct Answer: B — 15 km/h

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Q. A boat travels 30 km downstream in 2 hours. What is the speed of the current if the speed of the boat in still water is 15 km/h?

A. 2.5 km/h
B. 5 km/h
C. 7.5 km/h
D. 10 km/h

Solution

Speed downstream = distance/time = 30/2 = 15 km/h. Speed of current = speed downstream - speed of boat = 15 - 15 = 0 km/h.

Correct Answer: B — 5 km/h

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Q. A boat travels 30 km upstream and 30 km downstream in a total time of 6 hours. If the speed of the boat in still water is 10 km/h, what is the speed of the current?

A. 2 km/h
B. 3 km/h
C. 4 km/h
D. 5 km/h

Solution

Let speed of current = x. Time upstream = 30/(10-x), downstream = 30/(10+x). Total time = 6 hours. Solving gives x = 2 km/h.

Correct Answer: A — 2 km/h

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Q. A boat travels across a river with a speed of 4 m/s relative to the water. If the river flows at 3 m/s, what is the resultant speed of the boat relative to the riverbank?

A. 3 m/s
B. 4 m/s
C. 5 m/s
D. 7 m/s

Solution

Resultant speed = √(4^2 + 3^2) = √(16 + 9) = √25 = 5 m/s.

Correct Answer: C — 5 m/s

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Q. A boat travels across a river with a speed of 8 km/h relative to the water. If the river flows at 6 km/h, what is the speed of the boat relative to the riverbank?

A. 8 km/h
B. 10 km/h
C. 14 km/h
D. 6 km/h

Solution

Speed of boat relative to riverbank = √(8^2 + 6^2) = √(64 + 36) = √100 = 10 km/h.

Correct Answer: B — 10 km/h

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Q. A boat travels upstream at 4 km/h and downstream at 6 km/h. What is the speed of the current?

A. 1 km/h
B. 2 km/h
C. 3 km/h
D. 4 km/h

Solution

Let the speed of the current be x. Then, 4 + x = 6 - x. Solving gives x = 2 km/h.

Correct Answer: B — 2 km/h

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Q. A body is moving in a circular path of radius 4 m with a constant speed of 8 m/s. What is the net force acting on the body if its mass is 2 kg?

A. 4 N
B. 8 N
C. 16 N
D. 32 N

Solution

Centripetal force F = m(v²/r) = 2(8²/4) = 32 N.

Correct Answer: C — 16 N

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Q. A body is moving in a circular path with a radius of 10 m and completes one revolution in 5 seconds. What is its linear speed?

A. 2π m/s
B. 4π m/s
C. 10 m/s
D. 20 m/s

Solution

Linear speed (v) = Circumference / Time = (2π(10)) / 5 = 4π m/s.

Correct Answer: A — 2π m/s

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Q. A body is thrown vertically upwards with a speed of 20 m/s. How high will it rise? (g = 10 m/s²)

A. 20 m
B. 40 m
C. 30 m
D. 10 m

Solution

Using v² = u² - 2gh, 0 = (20)² - 2*10*h, h = 20 m.

Correct Answer: B — 40 m

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Q. A body is thrown vertically upwards with a speed of 20 m/s. How high will it rise before coming to rest?

A. 20 m
B. 40 m
C. 10 m
D. 30 m

Solution

Using the formula h = v²/(2g), where g = 10 m/s², h = (20)²/(2*10) = 20 m.

Correct Answer: B — 40 m

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Q. A body is thrown vertically upwards with a velocity of 20 m/s. How high will it rise before coming to rest? (g = 10 m/s²)

A. 20 m
B. 40 m
C. 10 m
D. 30 m

Solution

Using v² = u² - 2gh, 0 = (20)² - 2*10*h; h = 20 m.

Correct Answer: C — 10 m

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Q. A body moves in a straight line with a uniform acceleration of 2 m/s². If its initial velocity is 5 m/s, what will be its velocity after 10 seconds?

A. 25 m/s
B. 20 m/s
C. 15 m/s
D. 10 m/s

Solution

Final velocity = initial velocity + acceleration * time = 5 + 2 * 10 = 25 m/s.

Correct Answer: A — 25 m/s

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Q. A body moves in a straight line with an initial velocity of 10 m/s and accelerates at 2 m/s². What will be its velocity after 5 seconds?

A. 20 m/s
B. 25 m/s
C. 30 m/s
D. 35 m/s

Solution

Final velocity (v) = u + at = 10 + 2*5 = 20 m/s.

Correct Answer: C — 30 m/s

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