Home
Class 11
PHYSICS
A monkey of mass 'm' climbs up to a rope...

A monkey of mass `'m'` climbs up to a rope hung over a fixed pulley with an acceleration `g//4`. The opposite end of the rope is tied to a block of mass `M` lying on a rough horizontal plane. The coefficient of friction between the block and horizontal plane is `mu`. Find the tension in the rope.

Text Solution

Verified by Experts

`a_("monkey"//"rope")=g//4`
Let acceleration of `M=a_(0)`
So, acceleration of rope `=a_(0)`
`veca_("monkey")=veca_("monkey"//"rope")+veca_("rope")=(a_(0)-g//4)`
Now for mass `M`, `T-mu Mg=Ma_(0)`……(`1`)
For monkey `mg-T=m(a_(0)-g//4)`......(`2`)
From equation (`1`) and (`2`)
`mg-mu Mg=a_(0)(M+m)-(mg)/(4)`
`rArr a_(0)=((5m)/(4)-muM)g//(M+m)=((5m-4muM)g)/(4(M+m))`
`:. T=(M(5m-4mu M)g)/(4(M+m))+mu Mg`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

A monkey of mass 'm' climbs up to a rope hung over a fixed pulley with an acceleration relative to the rope g/4. The opposite end of the rope is tied to a bock of mass M lying on a rough horizontal plane. The coeffient of friction between the block and horizontal plane is mu . Find the tension in the rope

A monkey of mass m climbs up to a rope hung over a fixed pulley. The opposite end of the rope is tied to a weight of mass M lying on a horizontal plane. Neglecting the friction, find the acceleration of both the bodies (relative to the plane) and the tension of the rope for the three cases: (i) The monkey does not move with respect to the rope (ii) The monkey moves upwards with respect to the rope with acceleration a. (iii) The monkey moves downwards with respect to the rope, with acceleration a.

Knowledge Check

  • A block of mass m is pulled by a force of constant power P placed on a rough horizontal plane. The friction coefficient between the block and the surface is mu . Then

    A
    The maximum velocity of the block during the motion is `(P)/(mumg)`
    B
    The maximum velocity of the block during the motion is `(P)/(2mumg)`
    C
    The block's speed is never decreasing and finally becomes constant
    D
    The speed of the block first increases to a maximum value and then decreases

  • A cat of mass m = 1 kg climbs to a rope hung over a leight frictionless pulley. The opposite end of the rope is tied to a weight of mass M = 2m lying on a smooth horizontal plane. What is the tension of the rope where the cat move upwards with in acceleration a = 2 m//s^(2) relative to the rope ?

    A
    2 N
    B
    12N
    C
    8N
    D
    4N

  • A monkey of mass m clings a rope to a slung over a fixed pulley .The opposite end of the rope is tried to a weight of mass M tying on a horizontal table is mu Find the acceleration of weight and the tension of the rope for two cases .The monkey move downward with respect to the rope with an acceleration b. The tension of rope is

    A
    `(Mm(mu g+g +b))/(M +m)`
    B
    `(Mm(mu g-g +b))/(M +m)`
    C
    `(Mm(mu g+g -b))/(M +m)`
    D
    `(Mm(mu g-g -b))/(M +m)`

    • Similar Questions

    Explore conceptually related problems

    A monkey of massm clings to a rope slung over a fixed pulley. The opposite end of the rope is tied to a weight of mass M lying on a horizontal plat (Fig.). Neglecting friction find the acceleration of both bodies (relative to the plate) and the tension of the rope for the three cases: (1) the monkey does not move with respect to the rope, (2) the monkey moves upwards with respect to the rope with acceleration b, (3) the monkey moves downwards with respect to the rope with an acceleration b.

    A monkey of mass m clings a rope to a slung over a fixed pulley .The opposite end of the rope is tried to a weight of mass M tying on a horizontal table is mu Find the acceleration of weight and the tension of the rope for two cases .The monkey move downward with respect to the rope with an acceleration b. The acceleration of weight is

    A block of mass m is placed at rest on an inclination theta to the horizontal.If the coefficient of friction between the block and the plane is mu , then the total force the inclined plane exerts on the block is

    A block of mass m slides down an inclined plane which makes an angle theta with the horizontal. The coefficient of friction between the block and the plane is mu . The force exerted by the block on the plane is

    A block of mass m is pulled by a constant powert P placed on a rough horizontal plane. The friction coefficient the block and surface is mu . The maximum velocity of the block is.

    Home
    Profile