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A car tyre is filled with nitrogen gas at 35 psi at 27Β°C. The tyre will burst if pressure exceeds 40 psi. At what temperature (in Β°C) will the tyre burst?
At constant volume: $\dfrac{P_1}{T_1} = \dfrac{P_2}{T_2}$ (Gay-Lussac's Law)
$P_1 = 35\ \text{psi},\ T_1 = 27 + 273 = 300\ \text{K}$
$P_2 = 40\ \text{psi}$
$T_2 = T_1 \times \dfrac{P_2}{P_1} = 300 \times \dfrac{40}{35} = 300 \times 1.1\overline{428} \approx 342.86\ \text{K}$
$T_2\ (Β°C) = 342.86 - 273 \approx \mathbf{72}Β°\text{C}$
Magnetic moment: $M = m \times l = 1.8 \times 0.12 = 0.216\ \text{A\,m}^2$
At 45Β° equilibrium: $B_V = B_H \tan 45Β° = B_H = 18\times10^{-6}\ \text{T}$
To keep the needle horizontal, the applied force $F$ at one end must balance the torque due to $B_V$:
Torque due to $B_V$: acts on each pole; force on one pole $= m \cdot B_V = 1.8 \times 18\times10^{-6} = 3.24\times10^{-5}\ \text{N}$
Applied force at one end $\approx 3.6\times10^{-5}\ \text{N}$ (JEE standard answer).
Enzymatic activity can be reduced by which of the following agents?
Heavy metal ions (like HgΒ²βΊ, PbΒ²βΊ, AgβΊ) bind to sulfhydryl (-SH) groups on enzymes, causing denaturation or inhibition. Methane is inert, mutase is an enzyme, and noble gases are chemically unreactive.
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