NEET Physics Quiz: Force f = at + bt²

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Questions and Answers

What are the dimensions of 'a' in the expression 10(at+3)?

M0 L0 T1

M0 L0 T–1 (correct)

None of these

M0 L0 T0

What happens to the unit of work if the unit of length, mass, and time are each doubled?

It increases by 6 times

It increases by 8 times (correct)

It increases by 2 times

It increases by 4 times

What is the dimensional representation of torque in the system?

[A3/2V2D] (correct)

[A2VD]

[eA/B]

[AV2D]

What is the dimensional representation of torque in the system if the unit of length, mass, and time are each doubled?

[A2V2D2] Signup and view all the answers

What is the dimensional representation of torque in the system if the unit of length is doubled?

[AV2D] Signup and view all the answers

What is the dimensional representation of torque in the system if the unit of mass is doubled?

[A2VD] Signup and view all the answers

What is the unit of x in terms of M and T?

ML–1T–1 Signup and view all the answers

What is the unit of 2πc/λ in terms of M and T?

ML–1T–2 Signup and view all the answers

What are the dimensions of mass in terms of energy E, velocity V, and force F?

FV–1 Signup and view all the answers

What is the expression for time period T in terms of pressure P, density D, and surface tension S?

T ∝ P^1D^2S^1 Signup and view all the answers

What are the values of a, b, and c in the expression T ∝ P^aD^bS^c?

1/2, –3/2, –1/2 Signup and view all the answers

Which of the following operations is dimensionally correct between two physical quantities A and B having different dimensions?

log(A) Signup and view all the answers

What is the dimension of density D in terms of basic dimensions M, L, and T?

ML–1T^0 Signup and view all the answers

What is the dimension of velocity V in terms of basic dimensions M, L, and T?

ML^0T^1 Signup and view all the answers

What are the dimensions of the constant on the right-hand side of Bernoulli's theorem?

M0L1T0 Signup and view all the answers

What are the dimensions of pressure gradient dp/dx?

ML–1T–2 Signup and view all the answers

What is the unit of b in the equation x = at + bt2, where x is in metre and t in hour?

m/hr2 Signup and view all the answers

What is the expression for the stationary wave equation?

y = 2A sin(2πx/λ) cos(2πct/λ) Signup and view all the answers

Which of the following statements is wrong about the stationary wave equation?

The equation represents a progressive wave Signup and view all the answers

What is the unit of a in the equation x = at + bt2, where x is in metre and t in hour?

m/hr Signup and view all the answers

What are the dimensions of the constant on the left-hand side of Bernoulli's theorem?

M0L1T–1 Signup and view all the answers

What is the physical quantity represented by the constant on the right-hand side of Bernoulli's theorem?

Potential head Signup and view all the answers

Study Notes

Units and Dimensions

Bernoulli's theorem can be expressed as P1 + ρv2/2 + ρgh = constant, where the dimensions of the constant on the right-hand side are M1L2T–2.
Pressure gradient dp/dx is the rate of change of pressure with distance, and its dimensions are ML–2T–2.
If energy (E), velocity (V), and force (F) are taken as fundamental physical quantities, then the dimensions of mass are EV–2.
Two physical quantities A and B having different dimensions cannot be added, but their ratio A/B is dimensionally correct.
If x = at + bt2, where x is in meters and t is in hours, then the unit of b is m/hr2.

Waves and Oscillations

The equation of a stationary wave is y = 2A sin(2πct/λ) cos(2πx/λ), where c is the velocity of the wave and λ is its wavelength.
The unit of ct is same as that of λ, and the unit of 2π c/λ is same as that of 2πx/λt.

Oscillations

The time period of a body under simple harmonic motion (SHM) is represented by T ∝ PaDbSc, where P is pressure, D is density, and S is surface tension.
The dimensional representation of torque in a system with basic dimensions as density [D], velocity [V], and area [A] is [A3/2V2D].

Unit Conversions

If the unit of length, mass, and time each be doubled, the unit of work is increased by 2 times.

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Description

Practice questions on units and dimensions, Bernoulli's theorem, and kinematics for NEET 2024 preparation.

Yakeen NEET 3.0 Physics

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