The position of a particle moving on x-axis is given by x(t) = A sin + B + + D, where t is time. The dimension of is [2025]

Question

The position of a particle moving on x-axis is given by x(t) = A sin t + B $\cos^{2} t$ + $C t^{2}$ + D, where t is time. The dimension of $\frac{A B C}{D}$ is [2025]

Smart Achievers · Accepted Answer

(3)

Dimension [x(t)] = [L]

[A] = [L]

[B] = [L]

[C] = [ $L T^{- 2}$ ]

[D] = [L]

$[\frac{A B C}{D}] = [\frac{L \times L \times L T^{- 2}}{L}] = [L^{2} T^{- 2}]$

Solution

Q.
The position of a particle moving on x-axis is given by x(t) = A sin t + B $\cos^{2} t$ + $C t^{2}$ + D, where t is time. The dimension of $\frac{A B C}{D}$ is [2025]

1 L

2 $L^{3} T^{- 2}$

3 $L^{2} T^{- 2}$

4 $L^{2}$

Ans.
(3)

Dimension [x(t)] = [L]

[A] = [L]

[B] = [L]

[C] = [ $L T^{- 2}$ ]

[D] = [L]

$[\frac{A B C}{D}] = [\frac{L \times L \times L T^{- 2}}{L}] = [L^{2} T^{- 2}]$

Want Us to Email you About Special Offers & Updates?

Solution

Q. The position of a particle moving on x-axis is given by x(t) = A sin t + B cos2t + Ct2+ D, where t is time. The dimension of ABCD is [2025]

1 L

2 L3T–2

3 L2T–2

4 L2