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?
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.
APPEARS IN
संबंधित प्रश्न
Answer in Brief:
Part of a racing track is to be designed for curvature of 72m. We are not recommending the vehicles to drive faster than 216 kmph. With what angle should the road be tilted? By what height will its outer edge be, with respect to the inner edge if the track is 10 m wide?
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)
A metallic ring of mass 1 kg has a moment of inertia 1 kg m2 when rotating about one of its diameters. It is molten and remolded into a thin uniform disc of the same radius. How much will its moment of inertia be, when rotated about its own axis.
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.
For a body moving with constant speed in a horizontal circle, which of the following remains constant?
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 car moves at a speed of 36 km hr-1 on a level road. The coefficient of friction between the tyres and the road is 0.8. The car negotiates a curve of radius R. If g = 10 ms-2 , then the car will skid (or slip) while negotiating the curve, if the value of R is ____________.
A body of mass 10 kg is attached to a wire 0.3 m long. Its breaking stress is 4.8 × 107 N/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 ______.
In the case of conical pendulum, if T is the tension in the string and θ is the semivertical angle of cone, then the component of tension which balances the centrifugal force in equilibrium position is ______.
In the case of conical pendulum, if 'T' is the tension in the string and 'θ' is the semi-vertical angle of cone, then the component which provides necessary centripetal force is ______.
A flat curved road on highway has radius of curvature 400 m. A car rounds the curve at a speed of 24 m/s. The minimum value of coefficient of friction to prevent car from sliding is ______.
(take g = 10 m/s2)
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 ______.
What is banking of a road?
Why it is necessary 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 cyclist is undertaking horizontal circles inside a cylindrical well of radius 5 m. If the friction coefficient is 0.5, what should be the minimum speed of the cyclist?
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)
A body performing uniform circular motion has ______.
Why does a motorcyclist moving along a level curve at high speed have to lean more than a cyclist moving along the same curve at low speed?
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 × 10−2m/s, when it rests on 0.5 × 10−3 m thick layer of glycerin. Find the coefficient of viscosity of glycerin.
