AIEEE 2006 Mock Test

A particle located at $x=0$ at time $t=0$, starts moving along the positive $x$ -direction with a velocity $v$ that varies as $v=\alpha \sqrt{x}$. The displacement of the particle varies with time as:

A mass of $M\text{kg}$ is suspended by a weightless string. The horizontal force $F$ that is required to displace it until the string makes an angle of $45^{\circ }$ with the initial vertical direction is:

A bomb of mass $16\text{kg}$ at rest explodes into two pieces of masses $4\text{kg}$ and $12\text{kg}$. The velocity of the $12\text{kg}$ mass is $4\text{m/s}$. The kinetic energy of the other mass is:

A particle of mass $100\text{g}$ is thrown vertically upwards with a speed of $5\text{m/s}$. The work done by the force of gravity during the time the particle goes up is:

A whistle producing sound waves of frequencies $9500\text{Hz}$ and above is approaching a stationary person with speed $v\text{m/s}$. The velocity of sound in air is $300\text{m/s}$. If the person can hear frequencies up to a maximum of $10000\text{Hz}$, the maximum value of $v$ up to which he can hear the whistle is: