Home
Class 11
PHYSICS
Two bodies of masses m1 and m2 are conne...

Two bodies of masses `m_1 and m_2` are connected by a light string going over a smooth lilght pulley at the end of an incline. The mass `m_1` lies on the incline `m_2` hangs vertically. The system is at rest. Find the angle of the incline and the fore exerted by the incline on the body of mass `m_1`.

A

`sintheta=2m_2/m_1` , `N=m_1g cos theta`

B

`sintheta=m_2/m_1` , `N=m_1g cos theta`

C

`sintheta=m_2/m_1` , `N=m_1g sin theta`

D

`sintheta=m_2/m_1` , `N=4m_1g cos theta`

Text Solution

Verified by Experts

The correct Answer is:
B
ure shows the situation with the forces onn `m_1 and m_2` shown. Take the body of mass `m_2` as the system. The forces acting on it are

i. `m_2` g vertically downward (by the earth),
ii. T along the string up the incline (by the string),
N normal to the incline (by the incline).
As the string and the pulley are all light and smooth, the tension in the string is uniform everwhere. Hence, same T is used for the equations of `m_1 and m_2`.As the system is in equilibrium, these forces should add to zero.
Take components parallel to the incline,
`T=m_1 gcos (pi/2-theta)=m_1 g sin theta `.........ii
Taking comonents along the normal to the incline,
Taking components along the normal to the incline,
`N=m_1g cos theta` ............iii
ElimiN/Ating T form i and ii
`m_2g=m_1gsin theta`
or, `sintheta=m_2/m_1`
`giving ` theta= sin^-1 (m_2/m_1)`
From iii `N=m_1gsqrt(1- (m_2/m_1)2)`.
Promotional Banner

Similar Questions

Explore conceptually related problems

The two masses m_(1) and m_(2) are joined by a spring as shown. The system is dropped to the ground from a height. The spring will be

Two particles of masses m and M(Mgtm) are connected by a cord that passes over a massless, frictionless pulley. The tension T in the string and the acceleration a of the particles is

Two blocks of masses 2.0 kg and 3.0 kg are connected by light inextensible string. The string passes ove an ideal pulley pivoted to a fixed axel on a smooth incline place as shown in the figure. When the blocks are released, find magnitude of their accelerations.

Two masses m_(1) = 4.8 kg and m_(2) = 5 kg tied to a string are hanging over a light frictionless pully. What is the acceleration of masses when they are free to move ?

Two masses 8 kg and 12 kg are connected at the two ends of a light inextensible string that goes over a frictionless pulley. Find the acceleration of the masses, and the tension in the string when the masses are released.

Two masses 8 kg and 12 kg are connected at the two ends of a light inextensible string that goes over a frictionless pulley. Find the acceleration of the masses and the tension in the string when the masses are released.

Two blocks of masses m_(1) and m_(2) are connected by a massless pulley A, slides along th esmooth sides of a rectangular wedge of mass m, which rests on a smooth horizontal plane. Find the distance covered by the wedge on the horizontal plane till the mass m_(1) is lowered by the vertical distance h.

Three solids of masses m_(1),m_(2) and m_(3) are connected with weightless string in succession and are placed on a frictionless table. If the mass m_(3) is dragged with a force T , the tension in the string between m_(2) and m_(3) is

Two bars of masses m_(1) and m_(2) connected by a non - deformed light spring rest on a horizontal plane. The coefficient of friction between the bars and the surface is equal to mu . What minimum constant force has to be appled in the horizontal direction to the bar of mass m_(1) in order to shift the other bar?

In the fig. mass M=10gm. Is placed on an inclined plane. In order to keep it at rest, he value of mass m will be: