Home
Class 12
MATHS
A horse is tied to a post by a rope. If ...

A horse is tied to a post by a rope. If the horse moves along a circular path always keeping the rope tight, and describes `88` metres when it traces `72^@` at the centre, find the length of the rope.

Text Solution

Verified by Experts

The correct Answer is:
70 m
Let the post be at point P and PA be the length of the rope in tight position. Suppose the horse moves along the are AB so that `angle APB=72^@" and are "AB=88m`
Let r be the length of the rope, i.e., PA = r meters.
Now, `theta=72^@=(72xxpi/182)^R`
`=((2pi)/5)^R`
and `s=88m`
`:. theta=("Are")/("Radius")`
`or (2pi)/5=88/r`
`or r=88xx5/(2pi)=70m`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Concept Application Exercises 2.4|4 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Concept Application Exercises 2.5|16 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Concept Application Exercises 2.2|8 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE PUBLICATION|Exercise Archives (Numerical value type)|4 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|2 Videos

Similar Questions

Explore conceptually related problems

A horse running along a circular track of radius 27 ft passes over in 3 seconds an arc which subtends 70^@ at the centre. Find the distance the horse travels in half a minute.

A particle of mass m is tied with a rope and is rotated along a horizontal circular path. The length of the rope is r_(0) and the velocity of the particle is v_(0) . What amount of work should be done to decrease the length of the rope to r ?

Knowledge Check

  • A stone is tied with a massless rope and is rotated with uniform speed. Angular momentum of the stone is L . Keeping the angular velocity unchanged it the length of the rope is halved its angular momentum will be

    A
    `(L)/(4)`
    B
    `(L)/(2)`
    C
    L
    D
    2 L

  • A small mass m is rotating on a circular path of radius ton a smooth horizontal table with speed V. The centripetal force is provided by a light inextensible string tied to m and passing through a hole in the table at the centre of the circle and having a mass M hanging at its lower end. The mass M is suddenly increased to 8M. Find the new radius of the circle and the new velocity of m when the system attains equilibrium

    A
    2V and r/2
    B
    V/2 and 2r
    C
    2V and 2r
    D
    V/8 and 4r

    • Similar Questions

    Explore conceptually related problems

    As shown in Fig.7.40, the two sides of a step ladder BA and CA are 1.6 m long and hinged at A. A rope DE, 0.5 m is tied half way up. A weight 40 kg is suspended from a point F, 1.2 m from B along the ladder BA. Assuming the floor to be frictionless and neglecting the weight of the ladder, find the tension in the rope and forces exerted by the floor on the ladder. (Take g = 9.8 m//s^(2) )

    A stone of mass m tied with a thread is rotating along a horizontal circular path (force of gravity is neglected). The length of the thread is decreasing gradually in such a manner that the angular momentum of the stone remains constant with respect to the centre of the circle. If the tension in the thread is T= Ar^(n) , where A = constant , r = instantaneous radius of the circle, then find the value of n.

    A hours runs along a circle with a speed of 20 km/hr. A lantern is at the centre of the circle. A fence is along the tangent to the circle at the point at which the horse starts. Then find the speed with which the shadow of the horse moves along the fence at the moment when it covers 1/8 of the circle in km/hr.

    A piece of stone of mass 2 kg is tied with a thread of length 5 m and is rotated along a horizontal circular path. The thread can withstand a maximum tension of 30 N. What is the maximum velocity with which the stone can be rotated without snapping the thread? Also find the maximum number of revolutions that the stone can complete in one minute.

    One end of a 100 cm long rod is fixed. At its free end a screw is attached and the pitch of the screw is 0.5 mm. The rod can move along its length on turning the screw. The screw has a circular scale with 100 divisions. It moves by one small scale division of 0.5 mm per turn. At 20^(@)C , the pitch scale reads a little over zero and the circular scale reads 92. When the temperature is increased to 100^(@)C , the pitch scale reading changes to a little above 4 divisions and the circular scale reading is 72. Find the coefficient of linear expansion of the material of the rod.

    A particle with charge QC, tied at the end of an inextensible string of length R metre, revolves in a vertical plane. At the centre of the circular trajectory there is a fxied charge of magnitude QC. The mass of the moving charge M is such that Mg=(Q^(2))/(4pi epsi_(0)R^(2)) . If at the highest position of the particle, the tenstion of the string just vanishes, the horizontal velocity at the lowest point has to be

    Home
    Profile