The reading of a spring balance corresponds to $100 N$ while situated at the north pole and a body is kept on it. The weight record on the same scale if it is shifted to the equator, is $...........\,N$

(take, $g =10 m / s ^2$ and radius of the earth, $R =6.4 \times 10^3 m$ )

Which of the following statements is correct for any thermodynamic system?

$A$ convex lens of focal length $F$ produces a real image $n$ times the size of the object. The image distance is

Which of the following is true for the gaseous state?

$A$ parallel plate capacitor is charged to a potential difference of $100\,V$ and disconnected from the source of $emf$. $A$ slab of dielectric is then inserted between the plates. Which of the following three quantities change?
$(i)$ The potential difference
$(ii)$ The capacitance
$(iii)$ The charge on the plates

$A$ thermally insulated vessel contains an ideal gas of molecular mass $M$ and ratio of specific heats $\gamma$. It is moving with speed $v$ and is suddenly brought to rest. Assuming no heat is lost to the surroundings,its temperature increases by: