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An open knife edge of mass m is dropped from a height h on a wooden floor. If the blade penetrates upto the depth d into the wood, the average resistance offered by the wood to the knife edge is,
$ v^2 - V_0^2 = 2 ad , (v =0 ) and V_0 = \sqrt { 2gh } $ $ \therefore o = ( \sqrt { 2gh} )^2 + 2 (g-a) d \therefore a $
A force $F = Ay^2 + By + C$ acts on a body in the y-direction. The work done by this force during a displacement from y = -a to y = a is
$ W = \int Fdy $ $ = \int _{-a} ^{+2} (Ay^2 +By +C)dy $ $ = \left[ { Ay^3 \over 3} + { By^2 \over 2} + cy \right] _{-a}^{+a} $ $ = { 2Aa^3 \over 3} + 2Ca $
A spring with spring constant K when streched through 2cm the potential energy is U. If it is streched by 6cm. The potential energy will be......
$ Energy U \alpha x^2 ( k constant) $
If linear momentum of body is increased by 1.5%, its kinetic energy increases by……. %
$ K = { P^2 \over 2m } $ $ \therefore K \alpha p^2 $ ( m constant) $ \therefore { dk \over k } = 2 { dp \over p } $
With what velocity should a student of mass 40 kg run so that his kinetic energy becomes 160 J ?
$ k = {1 \over 2} mv^2 $ $ \therefore v = \sqrt { 2k \over m} $
A body of mass 1 kg is thrown upwords with a velocity 20 m/s. It momentarily comes to rest after a height 18m. How much energy is lost due to air friction. $(g = 10 m/s^2) $
Energy lost due to air friction $ = { 1 \over 2} mv^2 - mgh $
Two bodies of masses $m_1 and m_2$ have equal kinetic energies. If $P_1$ and $P_2$ are their respective momentum, what is ratio of $P_2 : P_1$ ?
$ P \alpha \sqrt m $ $ \therefore { p_1 \over p_2 } = { \sqrt {m_1} \over \sqrt {m_2} } $
The velocity of a body of mass 400 gm is $ ( -3 \hat i-4 \hat j) $ m/s. So its kinetic energy is ......
Find the value of $| \vec v |$ and than ,K.E = $ { 1\over 2} mv^2 $
A particle is moving under the influence of a force given by F = kx, where k is a constant and x is the distance moved. What energy (in joule) gained by the particle in moving from x = 1m to x = 3m ?
$ U = \int_1^3 kxdx $
A spring is compressed by 1 cm by a force of 4 N. Find the potential energy of the spring when it is compressed by 10 cm.
$ Spring constant K = { F \over x} , U = { 1 \over 2} kx^2 $
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The bank mixes NEET previous year questions (PYQs) with practice questions, each tagged with its exam appearances where applicable.