Two bodies of masses $m_1$ and $m_2$ are moving with same kinetic energy. If $P_1$ and $P_2$ are their respective momentum, the ratio $\frac{P_1}{P_2}$ is equal to
$\frac{m_1}{m_2}$
$\sqrt{\frac{m_2}{m_1}}$
$\sqrt{\frac{m_1}{m_2}}$
$\frac{m_1^2}{m_2^2}$
Pulley and spring are massless and the friction is absent everwhere. $5\,kg$ block is released from rest. The speed of $5\,kg$ block when $2\,kg$ block leaves the contact with ground is (take force constant of the spring $K = 40\,N/m$ and $g = 10\,m/s^2$ )
A block of mass $1\,kg$ is pushed up a surface inclined to horizontal at an angle of $30^o$ by a force of $10\,N$ parallel to the inclined surface (figure). The coefficient of friction between block and the incline is $0.1$. If the block is pushed up by $10\,m$ along the inclined calculate
$(a)$ work done against gravity
$(b)$ work done against force of friction
$(c)$ increases in potential energy
$(d)$ increases in kinetic energy
$(e)$ work done by applied force
A simple pendulum of mass $200\, gm$ and length $100\, cm$ is moved aside till the string makes an angle of $60^o$ with the vertical. The kinetic and potential energies of the bob, when the string is inclined at $30^o$ to the vertical, are
The total work done on a particle is equal to the change in its kinetic energy. This is applicable
A spring of force constant $K$ is first stretched by distance a from its natural length and then further by distance $b$. The work done in stretching the part $b$ is .............