A particle of mass m kg lies on a smooth plane inclined at an angle of 30° to the horizontal. The particle is attached to a light inextensible string which passes over a smooth pulley fixed at the top of the plane. Another particle of mass 3m kg is attached to the other end of the string and hangs freely. The system is released from rest with the string taut and the hanging part vertical. Find, in terms of m and g, (a) (b) (i) the acceleration of the system and the tension in the string, the magnitude of the reaction force exerted by the string on the pulley.

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Chapter1: Units, Trigonometry. And Vectors
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Answer detailly 3(i)

A particle of mass m kg lies on a smooth plane inclined at an angle of 30° to the horizontal. The
particle is attached to a light inextensible string which passes over a smooth pulley fixed at the
top of the plane. Another particle of mass 3m kg is attached to the other end of the string and
hangs freely.
The system is released from rest with the string taut and the hanging part vertical. Find, in terms
of m and g,
(a)
(b)
3.
(i)
the acceleration of the system and the tension in the string,
the magnitude of the reaction force exerted by the string on the pulley.
One end of a light inextensible string is fixed at a point A and a particle of mass m kg is attached
to the other end B. When the particle moves in a horizontal circle of radius r below A with
constant speed v m s', the string is inclined at an angle 0 to the downward vertical.
Show that v = gr tan 0.
(ii)
Transcribed Image Text:A particle of mass m kg lies on a smooth plane inclined at an angle of 30° to the horizontal. The particle is attached to a light inextensible string which passes over a smooth pulley fixed at the top of the plane. Another particle of mass 3m kg is attached to the other end of the string and hangs freely. The system is released from rest with the string taut and the hanging part vertical. Find, in terms of m and g, (a) (b) 3. (i) the acceleration of the system and the tension in the string, the magnitude of the reaction force exerted by the string on the pulley. One end of a light inextensible string is fixed at a point A and a particle of mass m kg is attached to the other end B. When the particle moves in a horizontal circle of radius r below A with constant speed v m s', the string is inclined at an angle 0 to the downward vertical. Show that v = gr tan 0. (ii)
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