Circular Dynamics & Newtons Laws of Motion

testindia testindia
Jan 25, 2025 - 20:21
0 25

1. A 100g bob is attached to a 1m-long string, which rotates around a vertical axis at a rate of (2/π) rev/s. What is the angle between the string and the vertical?

tan^-1(5/8)
tan^-1(3/5)
Cos^-1(3/5)
Cos^-1(5/8)

2. A cyclist travels at 14√3 m/s and navigates a circular turn with a radius of 20√3 m without losing traction. What is the angle of the cyclist's lean relative to the vertical?

30°
45°
60°
75°

3. Identify the incorrect statement:

Centrifugal force and centripetal force have equal magnitudes.
Centrifugal force acts along the radius, away from the center.
Centrifugal force exists in inertial frames of reference.
Centrifugal force is considered a pseudo-force because its origin cannot be explained.

4. Assertion: Driving a car or bus at high speed is challenging on rainy days. Reason: The coefficient of friction decreases due to the wet surface.

Choose the correct option:

Both assertion and reason are true, and the reason correctly explains the assertion.
Both assertion and reason are true, but the reason doesn't correctly explain the assertion.
Assertion is true, but the reason is false.
Both assertion and reason are false.

5. What is the maximum speed at which a car can navigate a 30m-radius turn on a road with a tire-road friction coefficient of 0.4?

9.84m/s
10.84m/s
7.84m/s
5.84m/s

6. A 5 kg block is initially at rest on a rough horizontal surface. A 24 N force is applied to it, and the coefficient of kinetic friction is 0.4. Assuming g = 9.8 m/s², what is the resulting acceleration of the block?

0.26 m/s²
0.39 m/s²
0.69 m/s²
0.88 m/s²

7. A 2 kg object moves according to the equation z(t) = 3t + 4t² + 5t³, where t is time in seconds. What is the force acting on the object at t = 2 seconds?"

136N
134N
158N
68 N

8. A firefighter needs to rescue a 40 kg injured person from a building using a rope with a maximum capacity of 100 kg. If the firefighter's mass is 80 kg, what will be their acceleration (assuming g = 9.8 m/s²)?

8.17 m/s²
9.8 m/s²
1.63 m/s²
17.97 m/s²

9. A 25 kg child slides down a rope suspended from a tall tree. Given that the frictional force opposing the child's descent is 200 N, calculate the child's acceleration (assuming g = 10 m/s²).

22.5 m/s²
8 m/s²
5 m/s²
2 m/s²

10. A 0.5 kg stone is attached to a 1-meter-long string and is moving in a circular path at a speed of 4 m/s. What is the tension in the string, measured in Newtons?

2
8
0.2
0.8