Advertisements
Advertisements
प्रश्न
Solve the following problem.
A car moves in a circle at a constant speed of 50 m/s and completes one revolution in 40 s. Determine the magnitude of the acceleration of the car.
Advertisements
उत्तर १
Given: v = 50 m/s, t = 40 s, s = 2πr
To find: acceleration (a)
Formulae:
i. v = `"s"/"t"`
ii. a = `"v"^2/"r"`
Calculation: From formula (i),
`50 = (2pi"r")/40`
∴ r = `(50 xx 40)/(2pi)`
∴ r = `1000/pi` cm
From formula (ii),
a = `"v"^2/"r" = 50^2/(1000//pi)`
a = `(5pi)/2 = 7.85 "m"//"s"^2`
The magnitude of acceleration of the car is 7.85 m/s2.
उत्तर २
Given: v = 50 m/s, t = 40 s,
To find: acceleration (a)
Formula: a = rω2 = vω
Calculation: From formula,
a = vω
`= "v"(("2"pi)/"t")`
`= 50((2 xx 3.142)/40)`
`= 5/2 xx 3.142`
∴ a = 7.85 m/s2
APPEARS IN
संबंधित प्रश्न
In U. C. M (Uniform Circular Motion), prove the relation `vec v = vec w xx vec r`, where symbols have their usual meanings.
A stone tied to the end of a string 80 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 14 revolutions in 25 s, what is the magnitude and direction of acceleration of the stone?
A particle starts from the origin at t = 0 s with a velocity of 10.0 `hatj "m/s"` and moves in the x-y plane with a constant acceleration of `(8.0 hati + 2.0 hatj) ms^(-2)`.
- At what time is the x-coordinate of the particle 16 m? What is the y-coordinate of the particle at that time?
- What is the speed of the particle at the time?
Why is the motion of a body moving with a constant speed around a circular path said to be accelerated?
Draw a neat labelled diagram for a particle moving in a circular path with a constant speed. In you diagram show the direction of velocity at any instant.
The motion of the moon around the earth in a circular path is an accelerated motion.
In a uniform circular motion, the speed continuously changes because of the direction of motion changes.
Which of the following remains constant in a uniform circular motion, Speed or Velocity, or both?
Answer the following question.
Show that its time period is given by, 2π`sqrt((l cos theta)/("g"))` where l is the length of the string, θ is the angle that the string makes with the vertical, and g is the acceleration due to gravity.
Define angular velocity.
Which one of the following is most likely not a case of uniform circular motion?
Which of the following graph represents uniform motion of a moving particle?
A uniform rod of length '6L' and mass '8 m' is pivoted at its centre 'C'. Two masses 'm' and ' 2m' with speed 2v, v as shown strikes the rod and stick to the rod. Initially the rod is at rest. Due to impact, if it rotates with angular velocity 'w1' then 'w' will be ________.
If a particle moves with uniform speed then its tangential acceleration will be ______.
The ratio of the angular speed of minute hand and hour hand of a watch is ____________.
A particle is moving in uniform circular motion with speed 'V' and radius 'R'. The angular acceleration of the particle is ______.
A particle is perfonning uniform circular motion. If 'θ', 'ω', 'α' and ' a' are its angular displacement, angular velocity, angular acceleration, and centripetal acceleration respectively, then which of the following is 'WRONG'?
It is possible to have objects moving with uniform velocity but non-uniform acceleration.
A point object moves along an arc of a circle of radius 'R'. Its velocity depends upon the distance covered 'S' as V = `Ksqrt(S)` where 'K' is a constant. If 'e' is the angle between the total acceleration and tangential acceleration, then
A body moving along a circular path of radius R with velocity v, has centripetal acceleration a. If its velocity is made equal to 2v. What will be the centripetal acceleration?
Earth also moves in circular orbit around sun once every year with on orbital radius of 1.5 × 1011 m. What is the acceleration of earth (or any object on the surface of the earth) towards the centre of the sun? How does this acceleration compare with g = 9.8 m/s2?
A disc of radius 5 cm rolls on a horizontal surface with linear velocity v = 1`hat"i"` m/s and angular velocity 50 rad/s. Height of particle from ground on rim of disc which has velocity in vertical direction is ______ cm.
A wet open umbrella is held upright and is rotated about the handle at a uniform rate of 21 revolutions in 44 s. If the rim of the umbrella is a circle of 1 metre in diameter and the height of the rim above the floor is 1.5 m, the drops of water spun off the rim and hit the floor at a horizontal ______ m from the umbrella.
A wheel is rotating at 900 rpm about its axis. When the power is cut off it comes to rest in 1 min. The angular retardation (assumed to be uniform (in rad s-1) is ______.
Two bodies of masses 10 kg and 5 kg moving in concentric orbits of radii R and r such that their periods are the same. Then the ratio between their centripetal accelerations is ______.
A thin uniform circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with an angular velocity ω. Another disc of same dimensions, but of mass `1/4`M is placed gently on the first disc co-axially. The. angular velocity of the system is ______.
A body of mass m is moving in circle of radius r with a constant speed v. The work done by the centripetal force in moving the body over half the circumference of the circle is ______.
The relationship between an object's linear velocity (v) and its angular velocity (ω) in a circular path of radius (r) is given by:
The relationship between an object's linear velocity (v) and its angular velocity (ω) in a circular path of radius (r) is given by:
Angular displacement is measured in which unit?
