A particle P of mass m is attached to a vertical axis by two strings A

1.	A particle P of mass m is attached to a vertical axis by two strings AP and BP of length l each. The separation AB = l. P rotates around the axis with an angular velocity ω. The tensions in the two strings are T1 and T2.(a) T1 = T2(b) T1 + T2 = mω2 l(c) T1 - T2 = 2mg(d) BP will remain taut only if ω ≥ √(2g/l).
Answer» Correct Answer is: (b, c, & d) △ABP is equilateral. Let T₁ and T₂ be the tensions in PA and PB respectively. T₁cos 60° = T₂cos 60° + mg or T₁ - T₂ = 2mg. T₁cos 30° + T₂cos 30° = mω² lcos 30° or T₁ + T₂ = mω² l. ∴ T₂ = 1/2 m [ω²l - 2g]. For T₂ ≥ 0, ω ≥ √(2g/l).

A particle P of mass m is attached to a vertical axis by two strings AP and BP of length l each. The separation AB = l. P rotates around the axis with an angular velocity ω. The tensions in the two strings are T1 and T2.(a) T1 = T2(b) T1 + T2 = mω2 l(c) T1 - T2 = 2mg(d) BP will remain taut only if ω ≥ √(2g/l).

Answer»

Correct Answer is: (b, c, & d)

△ABP is equilateral. Let T₁ and T₂ be the tensions in PA and PB respectively.

T₁cos 60° = T₂cos 60° + mg or T₁ - T₂ = 2mg.

T₁cos 30° + T₂cos 30° = mω² lcos 30° or T₁ + T₂ = mω² l.

∴ T₂ = 1/2 m [ω²l - 2g].

For T₂ ≥ 0, ω ≥ √(2g/l).

Discussion

No Comment Found

Related InterviewSolutions

Assume that the earth goes round the sun in a circular orbit with a constant speed of 30 km/s.(a) The average velocity of the earth from 1st Jan, 90 to 30th June, 90 is zero.(b) The average acceleration during the above period is 60 km/s2.(c) The average speed from 1st Jan, 90 to 31st Dec, 90 is zero.(d) The instantaneous acceleration of the earth points towards the sun.
The position vector of a particle in a circular motion about the origin sweeps out equal area in equal time.Its(a) velocity remains constant(b) speed remains constant(c) acceleration remains constant(d) tangential acceleration remains constant
The position vector of a particle in a circular motion about the origin sweeps out equal area in equal time. Its(a) velocity remains constant(b) speed remains constant(c) acceleration remains constant(d) tangential acceleration remains constant.
The safety speed of a vehicle on a curve horizontal road is(A) μrg(B) \(\sqrt{μrg}\)(C) μr2g(D) μ/(rg)2
A vehicle is moving along a circular road which is inclined to the horizontal at 10°. The maximum velocity with which it can move safely is 36 km/hr. Calculate the radius of the circular road.
Give the formulae of centripetal force.
Give the formula of inclination of banked road.
Formula of height of inclined road ?
If a particle moves with uniform speed then its tangential acceleration will be(A) \(\frac{v^2}{r}\) (B) zero (C) rω2 (D) infinite
If ωE and ωH are the angular velocities of the earth rotating about its own axis and the hour hand of the clock respectively, then(A) ωE = \(\frac{1}{4}\)ωH(B) ωE = 2 ωH(C) ωE = ωH(D) ωE = \(\frac{1}{2}\)ωE

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment