A particle is made to move from the origin in three spells of equal distances, first along the $x-$ axis, second parallel to $y-$ axis and third parallel to $z-$ axis. One of the forces acting on it is has constant magnitude of $50\,N$ and always acts along the direction of motion. Work done by this force in the three spells of motion are equal and total work done in all the three spells is $300\,J$. The final coordinates of the particle will be
$(2,\, 2,\, 2)\,m$
$(4,\, 4,\, 4)\,m$
$(6,\, 6,\, 6)\,m$
$(10,\, 10,\, 10)\,m$
A neutron makes a head-on elastic collision with a stationary deuteron. The fractional energy loss of the neutron in the collision is
A body of mass $m$ moving with velocity $v$ collides head on with another body of mass $2\, m$ which is initially at rest. The ratio of $K.E.$ of the colliding body before and after collision will be
In an elastic collision of two particles the following quantity is conserved
A curved surface is shown in figure. The portion $BCD$ is free of friction. There are three spherical balls of identical radii and masses. Balls are released from rest one by one from $A$ which is at a slightly greater height than $C$.
With the surface $AB$, ball $1$ has large enough friction to cause rolling down without slipping; ball $2$ has a small friction and ball $3$ has a negligible friction.
$(a)$ For which balls is total mechanical energy conserved ?
$(b)$ Which ball $(s)$ can reach $D$ ?
$(c)$ For ball which do not reach $D$, which of the balls can reach back $A$ ?
If $F = 2x^2 -3x -2$, then choose correct option