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 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 stone is tied to a string and whirled in a horizontal circle. If the radius of the circle is doubled, what happens to the centripetal force required to maintain the circular motion at the same speed?
A.It doubles
B.It remains the same
C.It halves
D.It quadruples
Solution
Centripetal force (F_c) = mv²/r. If r is doubled, F_c is halved for constant speed.
Q. A stone is tied to a string and whirled in a horizontal circle. If the radius of the circle is doubled, what happens to the centripetal force required to keep the stone moving in a circle at the same speed?
A.It doubles
B.It remains the same
C.It halves
D.It quadruples
Solution
Centripetal force (F_c) = mv²/r. If r is doubled, F_c is halved for the same speed.
Q. A stone is tied to a string and whirled in a horizontal circle. If the radius of the circle is doubled, what happens to the centripetal force required to maintain the stone's circular motion at the same speed?
A.It doubles
B.It remains the same
C.It halves
D.It quadruples
Solution
Centripetal force (F_c) = mv²/r. If r is doubled, F_c is halved for constant speed.
Q. A stone is tied to a string and whirled in a vertical circle of radius 1 m. What is the minimum speed at the top of the circle to keep the stone in circular motion?
A.1 m/s
B.2 m/s
C.3 m/s
D.4 m/s
Solution
At the top, centripetal force = weight. mv²/r = mg. v² = rg. v = √(1*9.8) ≈ 3.13 m/s.
