Let us consider a system of units in which mass and angular momentum are dimensionless. If length has dimension of $L$, which of the following statement ($s$) is/are correct ?
$(1)$ The dimension of force is $L ^{-3}$
$(2)$ The dimension of energy is $L ^{-2}$
$(3)$ The dimension of power is $L ^{-5}$
$(4)$ The dimension of linear momentum is $L ^{-1}$
Let us consider a system of units in which mass and angular momentum are dimensionless. If length has dimension of $L$, which of the following statement ($s$) is/are correct ?
$(1)$ The dimension of force is $L ^{-3}$
$(2)$ The dimension of energy is $L ^{-2}$
$(3)$ The dimension of power is $L ^{-5}$
$(4)$ The dimension of linear momentum is $L ^{-1}$
- [IIT 2019]
- A
$1,2,4$
- B
$1,2,3$
- C
$1,2$
- D
$1,3$
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Match List$-I$ with List$-II$.
List$-I$
List$-II$
$(A)$ Angular momentum
$(I)$ $\left[ ML ^2 T ^{-2}\right]$
$(B)$ Torque
$(II)$ $\left[ ML ^{-2} T ^{-2}\right]$
$(C)$ Stress
$(III)$ $\left[ ML ^2 T ^{-1}\right]$
$(D)$ Pressure gradient
$(IV)$ $\left[ ML ^{-1} T ^{-2}\right]$
Choose the correct answer from the options given below:
Match List$-I$ with List$-II$.
| List$-I$ | List$-II$ |
| $(A)$ Angular momentum | $(I)$ $\left[ ML ^2 T ^{-2}\right]$ |
| $(B)$ Torque | $(II)$ $\left[ ML ^{-2} T ^{-2}\right]$ |
| $(C)$ Stress | $(III)$ $\left[ ML ^2 T ^{-1}\right]$ |
| $(D)$ Pressure gradient | $(IV)$ $\left[ ML ^{-1} T ^{-2}\right]$ |
Choose the correct answer from the options given below:
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The dimensional formula $[ML^0T^{-3}]$ is more closely associated with
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