General Engineering Test 1 Nddc Scholarship

Answer: D. All of these

Torque is defined in several equivalent ways:

• As the product of force and moment arm (option A),

• As the turning effect of a force (option B),

• And mathematically as the cross product of position vector and force (option C):

\[ \text{Given: } \mu = 0.5,\; g = 10 \,\text{m/s}^2,\; m_1 = 3\,\text{kg},\; m_2 = 6\,\text{kg}\]

\[ f = \mu m_1 g = 0.5 \times 3 \times 10 = 15 \,\text{N}\]

\[ \text{For } m_2:\quad m_2 g - T = m_2 a\]

\[ \text{For } m_1:\quad T - f = m_1 a\]

\[ \Rightarrow m_2 g - f = (m_1 + m_2)a\]

\[ a = \dfrac{m_2 g - f}{m_1 + m_2}
= \dfrac{60 - 15}{3 + 6}
= \dfrac{45}{9}
= 5 \,\text{m/s}^2\]  

Correct option: B. material

Resistivity (ρ)(\rho) is a property of the material of the wire. It does not depend on the length or cross-sectional area. Those only affect the resistance RR, not the resistivity.

\[R= \rho \dfrac{L}{A}\]

Where:

• R = resistance

• \(\rho\) = resistivity (depends on material only)

• L = length of the wire

• A = cross-sectional area

Given 
Initial length: \( L = 30\,\text{cm} = 0.30\,\text{m} \) 
Extension: \( \Delta L = 30.5\,\text{cm} - 30\,\text{cm} = 0.5\,\text{cm} = 0.005\,\text{m} \) 
Force: \( F = 300\,\text{N} \)
Strain energy stored is given by:\[U = \dfrac{1}{2} F \Delta L = \dfrac{1}{2} \times 300 \times 0.005 = 0.75\,\text{J}\] Correct answer is \textbf{D. 0.75 J}

The formula for volume expansion is:\[ \Delta V = 3 \alpha V \Delta T \] Where: $$\alpha = 2.0 \times 10^{-5}$$ $\text{K}^{-1} V = 40 \, \text{cm}^3 $ $$\Delta T = 90^\circ \text{C} - 30^\circ \text{C} = 60 \, \text{K} $$ Substitute into the formula: $$ \Delta V = 3 \times (2.0 \times 10^{-5}) \times 40 \times 60 $$ \[ \Delta V = 6.0 \times 10^{-5} \times 2400 \] \[ \Delta V = 0.144 \, \text{cm}^3 \] \[ \boxed{0.144 \, \text{cm}^3} \]

Correct option: D. pressure law

The pressure law (also known as Gay-Lussac’s law) states that at constant volume, the pressure of a gas is directly proportional to its temperature.

Correct option: D. adiabatic expansion.

In an adiabatic expansion, a gas expands without heat exchange with its surroundings (Q = 0). Since the gas does work as it expands and no heat enters the system, its internal energy decreases, which leads to a drop in temperature.

Correct Answer: A. energy
Lenz's law states that the direction of an induced current is such that it opposes the change causing it. This ensures the conservation of energy, preventing the induced current from creating energy out of nothing.

Correct Answer is A. ML²T^-3I^-1

\[ \begin{aligned}
\text{EMF} &= \dfrac{\text{Work done}}{\text{Charge}} \\
          &= \dfrac{ML^2T^{-2}}{IT} \\
          &= ML^2T^{-3}I^{-1}
\end{aligned}\]  

\[ \begin{aligned}
I &= \dfrac{Q}{t} \Rightarrow Q = I \cdot t \\
Q &= 16\,\text{mA} \times 1\,\text{s} = 16 \times 10^{-3}\,\text{C} \\
e &= 1.6 \times 10^{-19}\,\text{C} \\
n &= \dfrac{Q}{e} = \dfrac{16 \times 10^{-3}}{1.6 \times 10^{-19}} = 1.00 \times 10^{17}
\end{aligned}\]