AIEEE 2003 (Physics) Mock Test

A carnot engine takes $3\times 10^6\text{cal}$ of heat from a reservoir at $627^{\circ }\text{C}$, and gives it to a sink at $27^{\circ }\text{C}$. The work done by the engine is:

A spring of spring constant $5\times 10^3\text{N/m}$ is stretched initially by $5\text{cm}$ from the unstretched position. Then the work required to stretch it further by another $5\text{cm}$ is:

A metal wire of linear mass density $9.8\text{g/m}$ is stretched with a tension of $10\text{kg-wt}$ between two rigid supports $1\text{metre}$ apart. The wire passes at its middle point between the poles of a magnet and it vibrates in resonance when carrying an alternating current of frequency $n$. The frequency $n$ of the alternating source is:

A tuning fork of known frequency $256\text{Hz}$ makes $5$ beats per second with the vibrating string of a piano. The beat frequency decreases to $2$ beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was:

A body executes simple harmonic motion. The potential energy (P.E.), the kinetic energy (K.E.) and total energy (T.E.) are measured as function of displacement $x$. Which of the following statement is true?