Motion In A Plane

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The potential energy of particle varies with distance x fixed a origin as $v = (\frac{A \sqrt{x}}{x + B})$ ; where A and B are constants. The dimensions of AB are

[ M L^5/2 T^-2 ]

[ M L² T^-² ]

[ M^3/2 L^3/2 T^-2 ]

[M L^7/2 T^-2 ]

Solution

[M L^7/2 T^-2 ]

Given;- v = $\frac{A \sqrt{x}}{x + B}$ .... (i)

Dimensions of v = dimensions of potential energy

= [ M¹ L² T^-2 ]

From equqtion (i)

Dimensions of B = Dimensions of x = [M^o L¹ T^o ]

∴ Dimensions of A = $\frac{dimension of v \times dimensions of (x + B)}{dimensions of \sqrt{x}}$

$= \frac{[M^{1} L^{2} T^{- 2}] [M^{o} L^{1} T^{o}]}{[M^{1} L^{\frac{1}{2}} T^{o}]}$

= [ M¹ L^5/2 T^-2 ]

Hence dimensions of AB

= [ M¹ L^5/2 T^-2 ] [ M^o L¹ T^o ]

= [ M L⁷^/2 T^-2 ]

Some More Questions From Motion in A Plane Chapter

Give three examples of scalar quantities.

Give three examples of vector quantities.

What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

Is a physical quantity, having a direction, necessarily a vector?

Name a quantity which is both scalar as well as vector.

Which of the followings is/are vector quantities: work, power, acceleration, mass, momentum?

Pick up the odd one from the following: force, linear momentum, mass, impulse.

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

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Motion In A Plane

The potential energy of particle varies with distance x fixed a origin as $v = (\frac{A \sqrt{x}}{x + B})$ ; where A and B are constants. The dimensions of AB are

[ M L^5/2 T^-2 ]

[ M L² T^-² ]

[ M^3/2 L^3/2 T^-2 ]

[M L^7/2 T^-2 ]

Some More Questions From Motion in A Plane Chapter

Give three examples of scalar quantities.

Give three examples of vector quantities.

What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

Is a physical quantity, having a direction, necessarily a vector?

Name a quantity which is both scalar as well as vector.

Which of the followings is/are vector quantities: work, power, acceleration, mass, momentum?

Pick up the odd one from the following: force, linear momentum, mass, impulse.

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

What are polar vectors?

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Motion In A Plane

The potential energy of particle varies with distance x fixed a origin as v = Axx + B; where A and B are constants. The dimensions of AB are [ M L5/2 T-2 ] [ M L2 T-2 ] [ M3/2 L3/2 T-2 ] [M L7/2 T-2 ]

Some More Questions From Motion in A Plane Chapter

Give three examples of scalar quantities.

Give three examples of vector quantities.

What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

Is a physical quantity, having a direction, necessarily a vector?

Name a quantity which is both scalar as well as vector.

Which of the followings is/are vector quantities: work, power, acceleration, mass, momentum?

Pick up the odd one from the following: force, linear momentum, mass, impulse.

Pick out the only vector quantities in the following list:Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list: force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

What are polar vectors?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

The potential energy of particle varies with distance x fixed a origin as $v = (\frac{A \sqrt{x}}{x + B})$ ; where A and B are constants. The dimensions of AB are

[ M L^5/2 T^-2 ]

[ M L² T^-² ]

[ M^3/2 L^3/2 T^-2 ]

[M L^7/2 T^-2 ]

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.