Question
$A$ force exerts an impulse $I$ on a particle changing its speed from $u$ to $2u$. The applied force and the initial velocity are oppositely directed along the same line. The work done by the force is
✓
Answer
$\mathrm{I}=\Delta \mathrm{P}$
$\mathrm{I}=2 \mathrm{mu}-(-\mathrm{mu})$
$\mathrm{I}=3 \mathrm{mu} \ldots(\mathrm{i})$
According to work energy theorem
$\mathrm{W}=\Delta \mathrm{T}$
$\mathrm{W}=\mathrm{T}_{\mathrm{f}}-\mathrm{T}_{\mathrm{i}}$
$\mathrm{W}=\frac{1}{2} \mathrm{m}(2 \mathrm{u})^{2}-\frac{1}{2} \mathrm{m}(-\mathrm{u})^{2}$
$\mathrm{W}=\frac{1}{2} \mathrm{m}\left(4 \mathrm{u}^{2}\right)-\frac{1}{2} \mathrm{mu}^{2}$
$\mathrm{w}=\frac{3 \mathrm{mu}^{2}}{2}$ $...(ii)$
From equation $(i)$ and $(ii)$
$\mathrm{W}=\frac{1}{2} \mathrm{Iu}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
In a resonance tube, the first resonance is obtained when the level of water in the tube is at $16\,cm$ from the open end. Neglecting end correction, the next resonance will be obtained when the level of water from the open end is .... $cm$
→A plane is flying horizontally at $98\, m/s$ and releases an object which reaches the ground in $10 \sec$. The angle made by object while hitting the ground is ......... $^o$
→The maximum and minimum amplitude of an amplitude modulated wave is $16\, V$ and $8\, V$ respectively. The modulation index for this amplitude modulated wave is $x \times 10^{-2}$. The value of $x$ is .........
→A capacitor with capacitance $5\,\mu F$ is charged to $5\,\mu C.$ If the plates are pulled apart to reduce the capacitance to $2\,\mu F,$ how much work is done?
→If $V$ denotes the potential difference across the plates of a capacitor of capacitance $C$, the dimensions of $C{V^2}$are
→The pressure at the bottom of a tank containing a liquid does not depend on
A body oscillates with $S.H.M.$ according to the equation $x=(5.0 \,m ) \cos \left[\left(2 \pi \,rad s ^{-1}\right) t+\pi / 4\right]$ At $t=1.5 \,s$, its acceleration is ....... $m / s ^2$
→A nucleus has a half-life of $30\; min$. At $3 \;PM$ its decay rate was measured as $120000 \,cps$. the decay rate ........... $\,cps$ at $5 \,PM$ ?
→A hollow lens is made of thin glass and in the shape of a double concave lens. It can be filled with air, water of refractive index $1.33$ or $CS _2$ of refractive index $1.6$. It will act as a diverging lens, if it is
→A road is $10\, m$ wide. Its radius of curvature is $50\, m$. The outer edge is above the lower edge by a distance of $1.5\, m$. This road is most suited for the velocity .......... $m/\sec$
→