Q. A mass m is attached to a string and is whirled in a horizontal circle. If the radius of the circle is halved, what happens to the tension in the string if the speed remains constant?
A.It doubles
B.It remains the same
C.It halves
D.It quadruples
Solution
Tension T = mv²/r. If r is halved, T doubles for constant speed.
Q. A mass m is attached to a string and is whirled in a vertical circle. At the highest point of the circle, what is the minimum speed required to keep the mass in circular motion?
A.√(g*r)
B.g*r
C.2g*r
D.g/2
Solution
At the highest point, the centripetal force is provided by the weight. Minimum speed = √(g*r).
Q. A mass m is attached to a string and is whirled in a vertical circle. At the highest point of the circle, the tension in the string is T. What is the expression for T?
A.T = mg
B.T = mg - mv²/r
C.T = mg + mv²/r
D.T = mv²/r
Solution
At the highest point, T + mg = mv²/r, thus T = mg - mv²/r.
Q. A mass m is attached to a string and is whirled in a vertical circle. At the highest point of the circle, what is the condition for the mass to just complete the circular motion?
A.Tension = 0
B.Tension = mg
C.Tension = 2mg
D.Tension = mg/2
Solution
At the highest point, the centripetal force is provided by the weight of the mass, so T + mg = mv²/r. For T = 0, mg = mv²/r.
Q. A mass m is attached to a string and is whirled in a vertical circle. At the top of the circle, the tension in the string is T. What is the expression for the tension at the bottom of the circle?
Q. A mass m is attached to a string of length L and is swung in a vertical circle. At the highest point of the circle, what is the minimum speed required to keep the mass in circular motion?
A.√(gL)
B.√(2gL)
C.gL
D.2gL
Solution
At the highest point, the centripetal force must equal the weight: mv²/L = mg, thus v = √(gL).
Q. A particle moves in a circular path of radius r with a constant angular acceleration α. What is the expression for the angular displacement θ after time t?
A.θ = αt²
B.θ = 0.5αt²
C.θ = αt
D.θ = 0.5αt
Solution
Angular displacement θ = 0.5αt² for constant angular acceleration.
Q. A person pushes a box with a force of 30 N, but the box does not move. If the coefficient of static friction is 0.6, what is the maximum static friction force?
A.18 N
B.30 N
C.36 N
D.60 N
Solution
The maximum static friction force is equal to the applied force when the box does not move, which is 30 N.
Q. A satellite is in a circular orbit around the Earth. If the radius of the orbit is 7000 km and the gravitational acceleration is 9.8 m/s², what is the speed of the satellite?
Q. A satellite is in a circular orbit around the Earth. If the radius of the orbit is 7000 km and the speed of the satellite is 7.9 km/s, what is the centripetal acceleration?
Q. A satellite is in a circular orbit around the Earth. If the radius of the orbit is doubled, what happens to the gravitational force acting on the satellite?
A.It doubles
B.It halves
C.It becomes four times
D.It becomes one-fourth
Solution
Gravitational force ∝ 1/r². If radius is doubled, force becomes 1/(2²) = 1/4.
Q. A stone is tied to a string and swung in a vertical circle. At the highest point, the tension in the string is 5 N and the weight of the stone is 10 N. What is the speed of the stone at the highest point if the radius of the circle is 2 m?
A.2 m/s
B.3 m/s
C.4 m/s
D.5 m/s
Solution
At the highest point, T + mg = mv²/r. 5 + 10 = (m*v²)/2. Solving gives v = 4 m/s.
