A particle of mass $m $ is moving in a horizontal circle of radius $r$ under a centripetal force equal to $ - K/{r^2}$, where $K$ is a constant. The total energy of the particle is
$\frac{K}{{2r}}$
$ - \frac{K}{{2r}}$
$ - \frac{K}{r}$
$\frac{K}{r}$
On complete combustion a litre of petrol gives off heat equivalent to $3\times 10^7\,J$. In a test drive, a car weighing $1200\,kg$ including the mass of driver, runs $15\,km$ per litre while moving with a uniform speed on a straight track. Assuming that friction offered by the road surface and air to be uniform, calculate the force of friction acting on the car during the test drive, if the efficiency of the car engine were $0.5$.
A body of mass $m= 10^{-2}$ $kg$ is moving in a medium and experiences a frictional force $F= -kv^2$. Its initial speed is $v_0= 10$ $ms^{-1}$. If, after $10\; s$, its energy is $\frac{1}{8}$ $mv_0^2$ the value of $k$ will be
A block of mass $m = 10\,kg$ rests on a horizontal table. The coefficient of friction between the block and the table is $0.05.$ When hit by a bullet of mass $50\,g$ moving with speed $v,$ that gets embedded in it, the block moves and comes to stop after moving a distance of $2\,m$ on the table. If a freely falling object were to acquire speed $\frac {v}{10}$ after being dropped from height $H,$ then neglecting energy losses and taking $g = 10\,ms^{-2},$ the value of $H$ is close to ................. $\mathrm{km}$
A particle is placed at the point $\mathrm{A}$ of a frictionless track $A B C$ as shown in figure. It is gently pushed toward right. The speed of the particle when it reaches the point $B$ is: $\left(\right.$ Take $g=10 \mathrm{~m} / \mathrm{s}^2$ ).
A block of mass $m$ is hung vertically from an elastic thread of force constant $\frac{{2mg}}{a}$ .Initially the thread was at its natural length and the block is allowed to fall freely. The work done on block by earth when it passes through the equilibrium position will be