Advertisements
Advertisements
प्रश्न
A thin walled hollow cylinder is rolling down an incline, without slipping. At any instant, without slipping. At any instant, the ratio "Rotational K.E.: Translational K.E.: Total K.E." is ______.
विकल्प
1 : 1 : 2
1 : 2 : 3
1 : 1 : 1
2 : 1 : 3
Advertisements
उत्तर
A thin walled hollow cylinder is rolling down an incline, without slipping. At any instant, without slipping. At any instant, the ratio "Rotational K.E.: Translational K.E.: Total K.E." is 1 : 1 : 2.
Explanation:
We know,
Rotational kinetic energy KR = `1/2 "mv"^2 "K"^2/"R"^2` ...(1)
Translational K. E. KT = `1/2 "mv"^2` ...(2)
Total kinetic energy K.ET = `1/2 "mv"^2 (1 + "K"^2/"R"^2)` ...(3)
`I = mR^2`
`m K^2 = m R^2`
`K^2/R^2 = 1` ...(4)
∴ KR : KT : K.ET = `1/2 "mv"^2 "K"^2/"R"^2 : 1/2 "mv"^2 : 1/2 "mv"^2 (1 + "K"^2/"R"^2)`
∴ KR : KT : K.ET = `cancel(1/2 "mv"^2) "K"^2/"R"^2 : cancel(1/2 "mv"^2) : cancel(1/2 "mv"^2) (1 + "K"^2/"R"^2)`
∴ KR : KT : K.ET = `"K"^2/"R"^2 : 1 : (1 + "K"^2/"R"^2)`
KR : KT : K.ET = 1 : 1 : (1 + 1) (From equation 4)
KR : KT : K.ET = 1 : 1 : 2
संबंधित प्रश्न
Answer in brief:
Why are curved roads banked?
Do we need a banked road for a two-wheeler? Explain.
On what factors does the frequency of a conical pendulum depend? Is it independent of some factors?
While driving along an unbanked circular road, a two-wheeler rider has to lean with the vertical. Why is it so? With what angle the rider has to lean? Derive the relevant expression. Why such a leaning is not necessary for a four wheeler?
Somehow, an ant is stuck to the rim of a bicycle wheel of diameter 1 m. While the bicycle is on a central stand, the wheel is set into rotation and it attains the frequency of 2 rev/s in 10 seconds, with uniform angular acceleration. Calculate:
- The number of revolutions completed by the ant in these 10 seconds.
- Time is taken by it for first complete revolution and the last complete revolution.
The coefficient of static friction between a coin and a gramophone disc is 0.5. Radius of the disc is 8 cm. Initially the center of the coin is 2 cm away from the center of the disc. At what minimum frequency will it start slipping from there? By what factor will the answer change if the coin is almost at the rim? (use g = π2m/s2)
Answer in Brief:
A flywheel used to prepare earthenware pots is set into rotation at 100 rpm. It is in the form of a disc of mass 10 kg and a radius 0.4 m. A lump of clay (to be taken equivalent to a particle) of mass 1.6 kg falls on it and adheres to it at a certain distance x from the center. Calculate x if the wheel now rotates at 80 rpm.
Starting from rest, an object rolls down along an incline that rises by 3 in every 5 (along with it). The object gains a speed of `sqrt 10` m/s as it travels a distance of `5/3` m along the incline. What can be the possible shape/s of the object?
A big dumb-bell is prepared by using a uniform rod of mass 60 g and length 20 cm. Two identical solid spheres of mass 25 g and radius 10 cm each are at the two ends of the rod. Calculate the moment of inertia of the dumb-bell when rotated about an axis passing through its centre and perpendicular to the length.
Does the angle of banking depend on the mass of the vehicle?
A bend in a level road has a radius of 100m. find the maximum speed which a car turning this bend may have without skidding if the coefficient of friction between the tires and road is 0.8.
A body weighing 0.5 kg tied to a string is projected with a velocity of 10 m/s. The body starts whirling in a vertical circle. If the radius of the circle is 0.8 m, find the tension in the string when the body is at the top of the circle.
Derive an expression for the kinetic energy of a rotating body with uniform angular velocity.
A rigid body rotates with an angular momentum L. If its kinetic energy is halved, the angular momentum becomes, ______
A particle undergoes uniform circular motion. The angular momentum of the particle remains conserved about, ______
When a mass is rotating in a plane about a fixed point, its angular momentum is directed along, ______
Give any two examples of torque in day-to-day life.
What is the relation between torque and angular momentum?
What are the rotational equivalents for the physical quantities, (i) mass and (ii) force?
A flywheel rotates with uniform angular acceleration. If its angular velocity increases from `20pi` rad/s to `40pi` rad/s in 10 seconds. Find the number of rotations in that period.
A ring and a disc of different masses are rotating with the same kinetic energy. If we apply a retarding torque τ on the ring, it stops after completing n revolution in all. If the same torque is applied to the disc, how many revolutions would it complete in all before stopping?
