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PHXI02:UNITS AND MEASUREMENTS

367306 A force is represented by \(F=a x^{2}+b t^{1 / 2}\) where \(x=\) distance and \(t=\) time. The dimensions of \(b^{2} / a\) are

1 \(\left[M L^{2} T^{-3}\right]\)

2 \(\left[M L^{-1} T^{-1}\right]\)

3 \(\left[M L T^{-2}\right]\)

4 \(\left[M L^{3} T^{-3}\right]\)

JEE - 2024

PHXI02:UNITS AND MEASUREMENTS

367307 Given that, \(y=A \sin \left[\left(\dfrac{2 \pi}{\lambda}(c t-x)\right)\right]\), where \(y\) and \(x\) are measured in metre. Which of the following statements is true?

1 The unit of \(\lambda\) is same as that of \(x\) and \(A\).

2 The unit of \(\lambda\) is same as that of \(x\) but not of \(A\).

3 The unit of \(c\) is same as that of \(\dfrac{2 \pi}{\lambda}\).

4 The unit of \((c t-x)\) is same as that of \(\dfrac{2 \pi}{\lambda}\).

PHXI02:UNITS AND MEASUREMENTS

367308 The equation of a circle is given by \(x^{2}+y^{2}=a^{2}\), where \(a\) is the radius. If the equation is modified to change the origin other than \((0,0)\), then find out the correct dimensions of \(A\) and \(B\) in a new equation.\((x-A t)^{2}+\left(y-\dfrac{t}{B}\right)^{2}=a^{2}\).The dimensions of \(t\) is given as \(\left[T^{-1}\right]\).

1 \(A=\left[L^{-1} T^{-1}\right], B=\left[L T^{-1}\right]\)

2 \(A=\left[L^{-1} T^{-1}\right], B=[L T]\)

3 \(A=[L T], B=\left[L^{-1} T^{-1}\right]\)

4 \(A=\left[L^{-1} T\right], B=\left[L T^{-1}\right]\)

JEE - 2023

PHXI02:UNITS AND MEASUREMENTS

367309 The force \(F\) is given in terms of time \(t\) and displacement \(x\) by the equation \(F=A \cos B x+\) \(C \sin D t\). The dimensional formula of \(D / B\) is

1 \(\left[M^{0} L^{0} T^{0}\right]\)

2 \(\left[M^{0} L^{0} T^{-1}\right]\)

3 \(\left[M^{0} L^{-1} T^{0}\right]\)

4 \(\left[M^{0} L^{1} T^{-1}\right]\)

PHXI02:UNITS AND MEASUREMENTS

367306 A force is represented by \(F=a x^{2}+b t^{1 / 2}\) where \(x=\) distance and \(t=\) time. The dimensions of \(b^{2} / a\) are

1 \(\left[M L^{2} T^{-3}\right]\)

2 \(\left[M L^{-1} T^{-1}\right]\)

3 \(\left[M L T^{-2}\right]\)

4 \(\left[M L^{3} T^{-3}\right]\)

JEE - 2024

PHXI02:UNITS AND MEASUREMENTS

367307 Given that, \(y=A \sin \left[\left(\dfrac{2 \pi}{\lambda}(c t-x)\right)\right]\), where \(y\) and \(x\) are measured in metre. Which of the following statements is true?

1 The unit of \(\lambda\) is same as that of \(x\) and \(A\).

2 The unit of \(\lambda\) is same as that of \(x\) but not of \(A\).

3 The unit of \(c\) is same as that of \(\dfrac{2 \pi}{\lambda}\).

4 The unit of \((c t-x)\) is same as that of \(\dfrac{2 \pi}{\lambda}\).

PHXI02:UNITS AND MEASUREMENTS

367308 The equation of a circle is given by \(x^{2}+y^{2}=a^{2}\), where \(a\) is the radius. If the equation is modified to change the origin other than \((0,0)\), then find out the correct dimensions of \(A\) and \(B\) in a new equation.\((x-A t)^{2}+\left(y-\dfrac{t}{B}\right)^{2}=a^{2}\).The dimensions of \(t\) is given as \(\left[T^{-1}\right]\).

1 \(A=\left[L^{-1} T^{-1}\right], B=\left[L T^{-1}\right]\)

2 \(A=\left[L^{-1} T^{-1}\right], B=[L T]\)

3 \(A=[L T], B=\left[L^{-1} T^{-1}\right]\)

4 \(A=\left[L^{-1} T\right], B=\left[L T^{-1}\right]\)

JEE - 2023

PHXI02:UNITS AND MEASUREMENTS

367309 The force \(F\) is given in terms of time \(t\) and displacement \(x\) by the equation \(F=A \cos B x+\) \(C \sin D t\). The dimensional formula of \(D / B\) is

1 \(\left[M^{0} L^{0} T^{0}\right]\)

2 \(\left[M^{0} L^{0} T^{-1}\right]\)

3 \(\left[M^{0} L^{-1} T^{0}\right]\)

4 \(\left[M^{0} L^{1} T^{-1}\right]\)

PHXI02:UNITS AND MEASUREMENTS

367306 A force is represented by \(F=a x^{2}+b t^{1 / 2}\) where \(x=\) distance and \(t=\) time. The dimensions of \(b^{2} / a\) are

1 \(\left[M L^{2} T^{-3}\right]\)

2 \(\left[M L^{-1} T^{-1}\right]\)

3 \(\left[M L T^{-2}\right]\)

4 \(\left[M L^{3} T^{-3}\right]\)

JEE - 2024

PHXI02:UNITS AND MEASUREMENTS

367307 Given that, \(y=A \sin \left[\left(\dfrac{2 \pi}{\lambda}(c t-x)\right)\right]\), where \(y\) and \(x\) are measured in metre. Which of the following statements is true?

1 The unit of \(\lambda\) is same as that of \(x\) and \(A\).

2 The unit of \(\lambda\) is same as that of \(x\) but not of \(A\).

3 The unit of \(c\) is same as that of \(\dfrac{2 \pi}{\lambda}\).

4 The unit of \((c t-x)\) is same as that of \(\dfrac{2 \pi}{\lambda}\).

PHXI02:UNITS AND MEASUREMENTS

367308 The equation of a circle is given by \(x^{2}+y^{2}=a^{2}\), where \(a\) is the radius. If the equation is modified to change the origin other than \((0,0)\), then find out the correct dimensions of \(A\) and \(B\) in a new equation.\((x-A t)^{2}+\left(y-\dfrac{t}{B}\right)^{2}=a^{2}\).The dimensions of \(t\) is given as \(\left[T^{-1}\right]\).

1 \(A=\left[L^{-1} T^{-1}\right], B=\left[L T^{-1}\right]\)

2 \(A=\left[L^{-1} T^{-1}\right], B=[L T]\)

3 \(A=[L T], B=\left[L^{-1} T^{-1}\right]\)

4 \(A=\left[L^{-1} T\right], B=\left[L T^{-1}\right]\)

JEE - 2023

PHXI02:UNITS AND MEASUREMENTS

367309 The force \(F\) is given in terms of time \(t\) and displacement \(x\) by the equation \(F=A \cos B x+\) \(C \sin D t\). The dimensional formula of \(D / B\) is

1 \(\left[M^{0} L^{0} T^{0}\right]\)

2 \(\left[M^{0} L^{0} T^{-1}\right]\)

3 \(\left[M^{0} L^{-1} T^{0}\right]\)

4 \(\left[M^{0} L^{1} T^{-1}\right]\)

PHXI02:UNITS AND MEASUREMENTS

367306 A force is represented by \(F=a x^{2}+b t^{1 / 2}\) where \(x=\) distance and \(t=\) time. The dimensions of \(b^{2} / a\) are

1 \(\left[M L^{2} T^{-3}\right]\)

2 \(\left[M L^{-1} T^{-1}\right]\)

3 \(\left[M L T^{-2}\right]\)

4 \(\left[M L^{3} T^{-3}\right]\)

JEE - 2024

PHXI02:UNITS AND MEASUREMENTS

367307 Given that, \(y=A \sin \left[\left(\dfrac{2 \pi}{\lambda}(c t-x)\right)\right]\), where \(y\) and \(x\) are measured in metre. Which of the following statements is true?

1 The unit of \(\lambda\) is same as that of \(x\) and \(A\).

2 The unit of \(\lambda\) is same as that of \(x\) but not of \(A\).

3 The unit of \(c\) is same as that of \(\dfrac{2 \pi}{\lambda}\).

4 The unit of \((c t-x)\) is same as that of \(\dfrac{2 \pi}{\lambda}\).

PHXI02:UNITS AND MEASUREMENTS

367308 The equation of a circle is given by \(x^{2}+y^{2}=a^{2}\), where \(a\) is the radius. If the equation is modified to change the origin other than \((0,0)\), then find out the correct dimensions of \(A\) and \(B\) in a new equation.\((x-A t)^{2}+\left(y-\dfrac{t}{B}\right)^{2}=a^{2}\).The dimensions of \(t\) is given as \(\left[T^{-1}\right]\).

1 \(A=\left[L^{-1} T^{-1}\right], B=\left[L T^{-1}\right]\)

2 \(A=\left[L^{-1} T^{-1}\right], B=[L T]\)

3 \(A=[L T], B=\left[L^{-1} T^{-1}\right]\)

4 \(A=\left[L^{-1} T\right], B=\left[L T^{-1}\right]\)

JEE - 2023

PHXI02:UNITS AND MEASUREMENTS

367309 The force \(F\) is given in terms of time \(t\) and displacement \(x\) by the equation \(F=A \cos B x+\) \(C \sin D t\). The dimensional formula of \(D / B\) is

1 \(\left[M^{0} L^{0} T^{0}\right]\)

2 \(\left[M^{0} L^{0} T^{-1}\right]\)

3 \(\left[M^{0} L^{-1} T^{0}\right]\)

4 \(\left[M^{0} L^{1} T^{-1}\right]\)

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