Kinetic Energy

Q. An alpha particle is accelerated from rest through a potential of V volts.Its final kinetic energy is

Q. Two identical pulses in a stretched string whose centres are initially $8\text{cm}$ apart, are moving towards each other as shown in the figure. The speed of each pulse is $2\text{cm/s}$. After $2\text{s}$, the total energy of the pulse will be

1. Zero
2. Purely kinetic
3. Purely potential
4. Partly kinetic and partly potential

Q. Escape velocity for a projectile at earth's surface is $V_e$. A body is projected from earth's surface with a velocity $2V_e$. The velocity of the body when it is at infinite distance from the center of the earth is?

1. $V_e$
   
2. $2V_e$
   
3. $\sqrt{2}{V}_e$
   
4. $\sqrt{3}{V}_e$
   

Q. A porter lifts a heavy suitcase of mass $80\text{kg}$ and at the destination lowers it down by a distance of $80\text{cm}$ with a constant velocity. Calculate the work done by the porter in lowering the suitcase. $(\text{take}g=9.8{\text{ms}}^{–2})$

1. $–627.2\text{J}$
2. $-62720.0\text{J}$
3. $784.0\text{J}$
4. $+627.2\text{J}$

Q.

The mass of cyclist together with the bike is 90 kg. Calculate the increase in kinetic energy if the speed increases from 6.0 km/h to 12 km/h.

Q. A nucleus of mass number A originally at rest emits $\alpha$-particle with speed v. The recoil speed of daughter nucleus is :

1. $\frac{4v}{A-4}$
2. $\frac{4v}{A+4}$
3. $\frac{v}{A-4}$
4. $\frac{v}{A+4}$

Q.

A rocket is fired ‘vertically’ from the surface of mars with a speed of 2 km s–1. If 20% of its initial energy is lost due to Martian atmospheric resistance, how far will the rocket go from the surface of mars before returning to it? Mass of mars = 6.4× 1023 kg; radius of mars = 3395 km; G = 6.67× 10^-11 N m² kg^–2.

Q. Name the type of energy [kinetic or potential] possessed by a moving bus.

Q. A positronium consists of an electron and a positron, revolving about their common centre of mass. Calculate the kinetic energy of the electron if the radius of circular path is equal to the radius of electron in ground state of a hydrogen atom.

1. $1.51\text{eV}$
2. $3.4\text{eV}$
3. $6.8\text{eV}$
4. $13.6\text{eV}$

Q. If mo and m are rest mass and moving mass of a body, then its kinetic energy is?

Q. A small disc and a large disc are connected by a belt. The small disc whose radius is 15 cm rotates at an angular speed of 360 rpm. The radius of large disc having mass 8 kg is 45 cm. The kinetic energy of large disc is nearly equal to ( Assume ${\pi }^2=10$)

1. 60 J
2. 64 J
3. 120 J
4. 45 J

Q. A ring of mass $m$ is rolling without slipping with linear speed $v$ as shown in figure. Four particles each of mass $m$ are also attached at points $\text{A, B, C}$ and $\text{D}$. Find total kinetic energy of the system.

1. $6m{v}^2$
   
2. $5m{v}^2$
   
3. $m{v}^2$
   
4. $3m{v}^2$
   

Q. An electron collides with a hydrogen atom in its ground state and excites it to $n=3$. The energy given to hydrogen atom in this inelastic collision is
[Neglect the recoiling of hydrogen atom]

1. $10.2\text{eV}$
2. $12.1\text{eV}$
3. $12.5\text{eV}$
4. None of these

Q. If the kinetic energy of a particle continuously increases with time,

1. the resultant force on it must be parallel to velocity at all instants.
2. the resultant force on it must be at an angle less than 90 degrees at all instants.
3. the resultant force on it must be at an angle equal to 90 degrees at all instants.
4. the resultant force on it must be at an angle greater than 90 degrees at all instants.

Q. Inside a fixed sphere of radius $R$ and uniform density $\rho$, there is spherical cavity of radius $\frac{R}{2}$ such that surface of the cavity passes through the centre of the sphere as shown in figure. A particle of mass $m$ is released from rest at centre $\text{B}$ of the cavity. Calculate velocity with which particle strikes the centre of the sphere. Neglect earth's gravity. Initially sphere and particle are at rest.

1. $\sqrt{\frac{2}{3}\pi G\rho R^2}$
2. $\sqrt{\frac{2}{3}\pi G{\rho }^2{R}^2}$
3. $\sqrt{\frac{2}{5}\pi G\rho R^2}$
4. $\sqrt{\frac{2}{3}{\pi }^2{G}^2{\rho }^2{R}^2}$

Q. State and prove principle of conservation of angular momentum.

Q. A car of mass 1000 kg accelerates from rest to $100km{h}^{-1}$ in 5 seconds. What is the average power of the car ?

1. $7.71\times {10}^{5}W$
2. $15.42\times {10}^{5}W$
3. $7.71\times {10}^{4}W$
4. $15.42\times {10}^{4}W$

Q.

A rocket is fired vertically with a speed of 5 km s^–1 from the earth’s surface. How far from the earth does the rocket go before returning to the earth? Mass of the earth = 6.0 × 10²⁴ kg; mean radius of the earth = 6.4 × 10⁶ m; G= 6.67 × 10^–11 N m² kg^–2.

Q. a satellite is moving with speed v in a circular orbit about the earth. an object of mass 2m is ejected from the satellite such that it just escapes from the gravitational pull of earth. at the time of ejection the kinetic energy of object is

Q. $kg{ms}^{-1}$ is the SI unit of

1. Force
2. Impulse
3. None of these
4. Angular velocity

Q. A rocket is launched with velocity of $10km{s}^{-1}$. If radius of earth is $R$ then maximum height attained by it will be:

1. $2R$
2. $3R$
3. $4R$
4. $5R$

Q. Derive relation between Kinetic Energy and Momentum .

Q. What is the work done to increase the velocity of a car from $30km{h}^{-1}$ to $60km{h}^{-1}$, if the mass of the car is $1500kg$?

Q. A bomb at rest explodes into two pieces of mass 2 kg and 4 kg respectively. If the relative velocity of pieces after explosion is 60 m/s, then kinetic energy of lighter particle is

विराम में स्थित एक बम द्रव्यमान क्रमशः 2 kg तथा 4 kg के दो भागों में विस्फोटित होता है। यदि विस्फोट के बाद भागों का सापेक्षिक वेग 60 m/s है, तब हल्के कण की गतिज ऊर्जा है

1. 1600 J
2. 800 J
3. 600 J
4. 1200 J

Q. An alpha-particle of mass $m$ suffers $1-$dimensional elastic collision with a nucleus at rest of unknown mass. It is scattered directly backwards losing, $64\%$ of its initial kinetic energy. The mass of the nucleus is:

1. $3.5m$
2. $2m$
3. $1.5m$
4. $4m$

Q. The ratio of rotational kinetic energy and translatory kinetic energy of a rolling circular disc is:

1. $4:1$
2. $1:2$
3. $2:1$
4. $1:4$

Q. A 1 kg mass has a kinetic energy of 1 joule when its speed is _______________.

1. $1m{s}^{-1}$
2. $4.4m{s}^{-1}$
3. $1.4m{s}^{-1}$
4. $0.45m{s}^{-1}$

Q. The linear momentum of a body is increased by 10 %. What is the percentage change in its kinetic energy?

1. 15%
2. 17%
3. 27%
4. 21%

Q. If $R$ is the radius of gyration of a body of mass $M$ and radius $r$, then the ratio of its rotational to translational kinetic energy in the rolling condition is :

1. $\frac{R^2}{R^2+r^2}$
2. $1$
3. $\frac{R^2}{r^2}$
4. $\frac{r^2}{R^2}$

Q. A ball is thrown from the top of a tower in vertically upward direction. The speed of ball at 10 m below the top of the tower is thrice of the speed at a point 10 m above the point of projection. The maximum height reached by the ball above the top of the tower will be

एक गेंद को एक मीनार के शिखर से ऊर्ध्वाधर ऊपर की ओर फेंका जाता है। मीनार के शिखर से 10 m नीचे गेंद की चाल प्रक्षेपण बिन्दु से 10 m ऊपर स्थित एक बिन्दु पर गेंद की चाल की तिगुनी है। मीनार के शिखर से गेंद द्वारा प्राप्त की गई अधिकतम ऊँचाई होगी

1. $\frac{20}{3}m$
2. 12.5 m
3. $\frac{80}{3}m$
4. 20 m