To find the velocity of the bead at point R, we can use the principle of conservation of mechanical energy.

Step 1: Determine the potential energy at point P.
Since the wire is frictionless and there is no mention of any other forces acting on the bead, we can assume that the only force acting on the bead is gravity. Therefore, the potential energy at point P can be calculated using the formula:
Potential energy at P = mass of the bead * acceleration due to gravity * height of point P above the reference point.
Given that the acceleration due to gravity (g) is 10 m/s^2 and the height of point P above the reference point is not provided, we cannot calculate the potential energy at point P.

Step 2: Determine the kinetic energy at point P.
The kinetic energy at point P can be calculated using the formula:
Kinetic energy at P = 0.5 * mass of the bead * velocity^2
Given that the initial velocity of the bead at point P is 5 m/s, we can calculate the kinetic energy at point P.

Step 3: Determine the kinetic energy at point R.
Since the wire is frictionless, the mechanical energy (sum of kinetic energy and potential energy) of the bead is conserved along the wire. Therefore, the kinetic energy at point R will be the same as the kinetic energy at point P.

Step 4: Calculate the velocity at point R.
Using the formula for kinetic energy at point R:
Kinetic energy at R = 0.5 * mass of the bead * velocity^2
Since the kinetic energy at point R is equal to the kinetic energy at point P, we can equate the two equations:
0.5 * mass of the bead * velocity^2 = 0.5 * mass of the bead * (5 m/s)^2
Simplifying the equation, we find:
velocity^2 = (5 m/s)^2
Taking the square root of both sides, we get:
velocity = 5 m/s

Therefore, the velocity of the bead at point R is 5 m/s.

Question

To find the velocity of the bead at point R, we can use the principle of conservation of mechanical energy.

Step 1: Determine the potential energy at point P.
Since the wire is frictionless and there is no mention of any other forces acting on the bead, we can assume that the only force acting on the bead is gravity. Therefore, the potential energy at point P can be calculated using the formula: 
Potential energy at P = mass of the bead * acceleration due to gravity * height of point P above the reference point.
Given that the acceleration due to gravity (g) is 10 m/s^2 and the height of point P above the reference point is not provided, we cannot calculate the potential energy at point P.

Step 2: Determine the kinetic energy at point P.
The kinetic energy at point P can be calculated using the formula:
Kinetic energy at P = 0.5 * mass of the bead * velocity^2
Given that the initial velocity of the bead at point P is 5 m/s, we can calculate the kinetic energy at point P.

Step 3: Determine the kinetic energy at point R.
Since the wire is frictionless, the mechanical energy (sum of kinetic energy and potential energy) of the bead is conserved along the wire. Therefore, the kinetic energy at point R will be the same as the kinetic energy at point P.

Step 4: Calculate the velocity at point R.
Using the formula for kinetic energy at point R:
Kinetic energy at R = 0.5 * mass of the bead * velocity^2
Since the kinetic energy at point R is equal to the kinetic energy at point P, we can equate the two equations:
0.5 * mass of the bead * velocity^2 = 0.5 * mass of the bead * (5 m/s)^2
Simplifying the equation, we find:
velocity^2 = (5 m/s)^2
Taking the square root of both sides, we get:
velocity = 5 m/s

Therefore, the velocity of the bead at point R is 5 m/s.

Knowee AI · Accepted Answer

To find the velocity of the bead at point R, we can use the principle of conservation of mechanical energy.

Step 1: Determine the potential energy at point P.
Since the wire is frictionless and there is no mention of any other forces acting on the bead, we can assume that the only force acting on the bead is gravity. Therefore, the potential energy at point P can be calculated using the formula: 
Potential energy at P = mass of the bead * acceleration due to gravity * height of point P above the reference point.
Given that the acceleration due to gravity (g) is 10 m/s^2 and the height of point P above the reference point is not provided, we cannot calculate the potential energy at point P.

Step 2: Determine the kinetic energy at point P.
The kinetic energy at point P can be calculated using the formula:
Kinetic energy at P = 0.5 * mass of the bead * velocity^2
Given that the initial velocity of the bead at point P is 5 m/s, we can calculate the kinetic energy at point P.

Step 3: Determine the kinetic energy at point R.
Since the wire is frictionless, the mechanical energy (sum of kinetic energy and potential energy) of the bead is conserved along the wire. Therefore, the kinetic energy at point R will be the same as the kinetic energy at point P.

Step 4: Calculate the velocity at point R.
Using the formula for kinetic energy at point R:
Kinetic energy at R = 0.5 * mass of the bead * velocity^2
Since the kinetic energy at point R is equal to the kinetic energy at point P, we can equate the two equations:
0.5 * mass of the bead * velocity^2 = 0.5 * mass of the bead * (5 m/s)^2
Simplifying the equation, we find:
velocity^2 = (5 m/s)^2
Taking the square root of both sides, we get:
velocity = 5 m/s

Therefore, the velocity of the bead at point R is 5 m/s.

A bead starts sliding from a point P on a frictionlesswire with initial velocity of 5 ms –1 . Find thevelocity of bead at point R (take g = 10 ms –2 )(1) 7 m/s(2) 5 2 m/s 4 mPRQ1.65 m(3) 6 2 m/s(4) 6 m/s

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