Advertisements
Advertisements
प्रश्न
A stone is fastened to one end of a string and is whirled in a vertical circle of radius R. Find the minimum speed the stone can have at the highest point of the circle.
Advertisements
उत्तर
Let m be the mass of the stone.
Let v be the velocity of the stone at the highest point.
R is the radius of the circle.
Thus, in a vertical circle and at the highest point,
we have :
\[\frac{\text{mv}^2}{\text{R}} = \text{mg}\]
\[ \Rightarrow \text{v}^2 = \text{Rg}\]
\[ \Rightarrow \text{v} = \sqrt{\text{Rg}}\]
APPEARS IN
संबंधित प्रश्न
A thin circular loop of radius R rotates about its vertical diameter with an angular frequency ω. Show that a small bead on the wire loop remains at its lowermost point for `omega <= sqrt(g/R)` .What is the angle made by the radius vector joining the centre to the bead with the vertical downward direction for `omega = sqrt("2g"/R)` ?Neglect friction.
When a particle moves in a circle with a uniform speed
Tow cars having masses m1 and m2 moves in circles of radii r1 and r2 respectively. If they complete the circle in equal time, the ratio of their angular speed ω1/ω2 is
A stone of mass m tied to a string of length l is rotated in a circle with the other end of the string as the centre. The speed of the stone is v. If the string breaks, the stone will move
A coin placed on a rotating turntable just slips. If it is placed at a distance of 4 cm from the centre. If the angular velocity of the turntable is doubled, it will just slip at a distance of
If the earth stop rotating, the apparent value of g on its surface will
Let θ denote the angular displacement of a simple pendulum oscillating in a vertical plane. If the mass of the bob is m, the tension is the string is mg cos θ
Assume that the earth goes round the sun in a circular orbit with a constant speed of 30 kms
The position vector of a particle in a circular motion about the origin sweeps out equal area in equal time. Its
(a) velocity remains constant
(b) speed remains constant
(c) acceleration remains constant
(d) tangential acceleration remains constant.
A car goes on a horizontal circular road of radius R, the speed increasing at a constant rate \[\frac{\text{dv}}{\text{dt}} = a\] . The friction coefficient between the road and the tyre is μ. Find the speed at which the car will skid.
What is the radius of curvature of the parabola traced out by the projectile in the previous problem at a point where the particle velocity makes an angle θ/2 with the horizontal?
Choose the correct option.
Select correct statement about the formula (expression) of moment of inertia (M.I.) in terms of mass M of the object and some of its distance parameter/s, such as R, L, etc.
In a certain unit, the radius of gyration of a uniform disc about its central and transverse axis is `sqrt2.5`. Its radius of gyration about a tangent in its plane (in the same unit) must be ______.
Choose the correct option.
Consider the following cases:
(P) A planet revolving in an elliptical orbit.
(Q) A planet revolving in a circular orbit.
Principle of conservation of angular momentum comes in force in which of these?
A wheel is subjected to uniform angular acceleration about its axis. The wheel is starting from rest and it rotates through an angle θ1, in first two seconds. In the next two seconds, it rotates through an angle θ2. The ratio θ1/θ2 is ____________.
The centripetal force of a body moving in a circular path, if speed is made half and radius is made four times the original value, will ____________.
An engine requires 5 seconds to go from a speed of 600 r.p.m. to 1200 r.p.m. How many revolutions does it make in this period?
In negotiating curve on a flat road, a cyclist leans inwards by an angle e with the vertical in order to ______.
A body is moving along a circular track of radius 100 m with velocity 20 m/s. Its tangential acceleration is 3 m/s2 then its resultant accelaration will be ______.
A bob is whirled in a horizontal plane by means of a string with an initial speed of ω rpm. The tension in the string is T. If speed becomes 2ω while keeping the same radius, the tension in the string becomes ______.
