The true length of a wire is $$3.678 \mathrm{~cm}$$. When the length of this wire is measured using instrument $$A$$, the length of the wire is $$3.5 \mathrm{~cm}$$. When the length of the wire is measured using instrument $$B$$, it is found to have length $$3.38 \mathrm{~cm}$$. Then, the
A body is moving along a straight line with initial velocity $$v_0$$. Its acceleration $$a$$ is constant. After $$t$$ seconds, its velocity becomes $$v$$. The average velocity of the body over the given time interval is
A closed water tank has cross-sectional area $$A$$. It has a small hole at a depth of $$h$$ from the free surface of water. The radius of the hole is $$r$$ so that $$r \ll \sqrt{\frac{A}{\pi}}$$. If $$p_o$$ is the pressure inside the tank above water level and $$p_a$$ is the atmospheric pressure, the rate of flow of the water coming out of the hole is ( $$\rho$$ is density of water)
$$100 \mathrm{~g}$$ of ice at $$0^{\circ} \mathrm{C}$$ is mixed with $$100 \mathrm{~g}$$ of water at $$100^{\circ} \mathrm{C}$$. The final temperature of the mixture is
[Take, $$L_f=3.36 \times 10^5 \mathrm{~J} \mathrm{~kg}^{-1}$$ and $$S_w=4.2 \times 10^3 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1} \text { ] }$$