मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Answer in brief: A uniform disc and a hollow right circular cone have the same formula for their M.I. when rotating about their central axes. Why is it so?

Advertisements
Advertisements

प्रश्न

Answer in brief:

A uniform disc and a hollow right circular cone have the same formula for their M.I. when rotating about their central axes. Why is it so?

टीपा लिहा
Advertisements

उत्तर

A uniform disc and a hollow right circular cone have the same formula for their moment of inertia.

`"MI" = 1/2mr^2`

This is due to the fact that when a hollow right circular cone is sliced along its slanting side and the metal is stretched out, the cone's surface becomes a circle. This shape is similar to that of a disc, which is a circular as well. As a result, they both share the same moment of inertia formula.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Rotational Dynamics - Exercises [पृष्ठ २४]

APPEARS IN

बालभारती Physics [English] Standard 12 Maharashtra State Board
पाठ 1 Rotational Dynamics
Exercises | Q 2.5 | पृष्ठ २४

संबंधित प्रश्‍न

A road is constructed part of a racing tracks to be designed with radius of curvature 72 m. We are not recommending the vehieles to drive faster than 216 kmph.. The coefficient of static friction between the tyres of a vehicle on this road is 0.8, will there be any lower speed limit? By how much can the upper speed limit exceed in this case?

(Given: r = 72 m, vo = 216 km/h, w = 10 m, θ = 78°4', h = 9.805 m)


Using the energy conservation, derive the expressions for the minimum speeds at different locations along a vertical circular motion controlled by gravity. Is zero speed possible at the uppermost point? Under what condition/s?


Using energy conservation, along a vertical circular motion controlled by gravity, prove that the difference between the extreme tensions (or normal forces) depends only upon the weight of the objects.


A block of mass m is moving on rough horizontal surface with momentum p. The coefficient of friction between the block and surface is µ. The distance covered by the block before it stops is [g =acceleration due to gravity)


For a body moving with constant speed in a horizontal circle, which of the following remains constant?


A cyclist with combined mass 80 kg goes around a curved road with a uniform speed 20 m/s. He has to bend inward by an angle `theta` = tan-1 (0.50) with the vertical. The force of friction acting at the point of contact of tyres and road surface is______.

[g = 10 m/s2 ]


A horizontal circular platform of mass 100 kg is rotating at 5 r.p.m. about vertical axis passing through its centre. A child of mass 20 kg is standing on the edge of platform. If the child comes to the centre of platform then the frequency of rotation will become ______.


A pendulum has length of 0.4 m and maximum speed 4 m/s. When the length makes an angle 30° with the horizontal, its speed will be ______.
`[sin  pi/6 = cos  pi/3 = 0.5 and "g" = 10 "m"//"s"^2]`


A body of mass 10 kg is attached to a wire 0.3 m long. Its breaking stress is 4.8 × 10N/m2. The area of cross-section of the wire is 10-6m2. The maximum angular velocity with which it can be rotated 111 a horizontal circle is ______.


A motorcyclist rides in a horizontal circle about central vertical axis inside a cylindrical chamber of radius 'r'. If the coefficient of friction between the tyres and the inner surface of chamber is 'µ', the minimum speed of motorcyclist to prevent him from skidding is ______.

('g' =acceleration due to gravity)


A particle executes uniform circular motion with angular momentum 'L'. Its rotational kinetic energy becomes half when the angular frequency is doubled. Its new angular momentum is ______.


If friction is made zero for a road, can a vehicle move safely on this road?


What is banking of a road? 


A curved road 5 m wide is to be designed with a radius of curvature 900 m. What should be the elevation of the outer edge of the road above the inner edge optimum speed of the vehicles rounding the curve is 30 m/s.


The centripetal acceleration of the bob of a conical pendulum is, in the usual notation, ______.


A string of length 0.5 m carries a bob of mass 0.1 kg at its end. If this is to be used as a conical pendulum of period 0.4 π sec, the angle of inclination of the string with the vertical is ______. (g = 10m/s2)


The radius of curvature of road is 60 m. If angle of banking is 27°, find maximum speed with which vehicle can tum along this curve. . (g = 9.8 m/s2)


Derive an expression for maximum speed moving along a horizontal circular track.


A horizontal force of 0.5 N is required to move a metal plate of area 10−2 m2 with a velocity of 3 × 102m/s, when it rests on 0.5 × 103 m thick layer of glycerin. Find the coefficient of viscosity of glycerin.


In case of well of death which is a vertical cylindrical wall of radius ‘r’ inside which vehicle is driven in horizontal circles. If ‘m’ is mass of vehicle, ‘V’ is the velocity and u, is the coefficient of static friction between the wheels of vehicle and walls then correct relation is ______.

[g = acceleration due to gravity]


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×