### Units And Dimension Mock Test 01

Quantity) | | List-II | | | :--- | :--- | :--- | :--- | | (Dimensional Formula) | | | | | A | Pressure

gradient | I | $[M^{0} L^{2} T^{-2}]$ | | B | Energy density | II | $[M^{1} L^{-1} T^{-2}]$ | | C | Electric Field | III | $[M^{1} L^{-2} T^{-2}]$ | | D | Latent heat | IV | $[M^{1} L^{1} T^{-3} A^{-1}]$ | Choose the correct answer from the options given below: - [ ] A-III, B-II, C-I, D-IV - [ ] A-II, B-III, C-IV, D-I - [x] A-III, B-II, C-IV, D-I - [ ] A-II, B-III, C-I, D-IV #### Question 6 - 29 January - Shift 2 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: $(x-A t)^{2}+(y-\frac{t}{B})^{2}=a^{2}$. The dimensions of $t$ is given as $[T^{-1}]$. - [ ] $A=[L^{-1} T], B=[LT^{-1}]$ - [x] $A=(LT], B=[L^{-1} T^{-1}]$ - [ ] $A=[L^{-1} T^{-1}], B=[LT^{-1}]$ - [ ] $A=[L^{-1} T^{-1}], B=[LT]$ #### Question 7 - 30 January - Shift 1 Electric field in a certain region is given by $\dot{E}=(\frac{A}{x^{2}} \hat{i}+\frac{B}{y^{3}} \hat{j})$. The SI unit of $A$ and $B$ are : - [ ] $Nm^{3} C^{-1} ; Nm^{2} C^{-1}$ - [x] $Nm^{2} C^{-1} ; Nm^{3} C^{-1}$ - [ ] $Nm^{3} C ; Nm^{2} C$ - [ ] $Nm^{2} C ; Nm^{3} C$ #### Question 8 - 30 January - Shift 2 Match List I with List II. | | List I | | List II | | :--- | :--- | :--- | :--- | | A | Torque | I. | $kg m^{-1} s^{-2}$ | | B | Energy density ath | II. | $kg ms^{-1}$ | | C | Pressure gradient | III. | $kg m^{-2} s^{-2}$ | | D | Impulse | IV. | $kg m^{2} s^{-2}$ | Choose the correct answer from the options given below: - [ ] A-IV, B-III, C-I, D-II - [ ] A-I, B-IV, C-III, D-II - [ ] A-IV, B-I, C-II, D-III - [x] A-IV, B-I, C-III, D-II #### Question 9 - 31 January - Shift 1 If $R, X_L$ and $X_C$ represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless: - [ ] $RX_L X_C$ - [x] $\frac{R}{\sqrt{X_L X_C}}$ - [ ] $\frac{R}{X_L X_C}$ - [ ] $R \frac{X_L}{X_C}$ #### Question 10 - 31 January - Shift 2 Match List-I with List-II. | | List-I | | List-II | | :--- | :--- | :--- | :--- | | A. | Angular

momentum | I | $[ML^{2} T^{-2}]$ | | B | Torque | II | $[ML^{-2} T^{-2}]$ | | C | Stress | III | $[ML^{2} T^{-1}]$ | | D | Pressure gradient | IV | $[ML^{-1} T^{-2}]$ | Choose the correct answer from the options given below: - [ ] A-I, B-IV, C-III, D-II - [x] A-III, B-I, C-IV, D-II - [ ] A-II, B-III, C-IV, D-I - [ ] A-IV, B-II, C-I, D-III #### Question 11 - 01 February - Shift 1 $(P+\frac{a}{V^{2}})(V-b)=R T$ represents the equation of state of some gases. Where $P$ is the pressure, $V$ is the volume, $T$ is the temperature and $a, b, R$ are the constants. The physical quantity, which has dimensional formula as that of $\frac{b^{2}}{a}$, will be : - [ ] Bulk modulus - [ ] Modulus of rigidity - [x] Compressibility - [ ] Energy density #### Question 12 - 01 February - Shift 2 If the velocity of light $c$, universal gravitational constant $G$ and planck's constant $h$ are chosen as fundamental quantities. The dimensions of mass in the new system is: - [ ] $[h^{\frac{1}{2}} c^{-\frac{1}{2}} G^{1}].$ - [ ] $[h^{1} c^{1} G^{-1}]$ - [ ] $[h^{-\frac{1}{2}} c^{\frac{1}{2}} G^{\frac{1}{2}}]$ - [x] $[h^{\frac{1}{2}} c^{\frac{1}{2}} G^{-\frac{1}{2}}]$