355421
Four particles \(A, B, C, D\) of mass \(\dfrac{m}{2}, m, 2 m, 4 m\), have same momentum, respectively. The particle with maximum kinetic energy is
1 \(C\)
2 \(A\)
3 \(D\)
4 \(B\)
Explanation:
\(K E=\dfrac{p^{2}}{2 m}\) For same momentum \((p), K E \propto \dfrac{1}{m}\) Therefore, the lightest particle will possess maximum kinetic energy. \(\therefore \) A possess maximum kinetic energy. So, correct option is (2).
JEE - 2024
PHXI06:WORK ENERGY AND POWER
355422
Two bodies are having kinetic energies in the ratio \(16: 9\). If they have same linear momentum, the ratio of their masses respectively is
1 \(4: 3\)
2 \(16: 9\)
3 \(3: 4\)
4 \(9: 16\)
Explanation:
Kinetic energy of a body is given by \(K=\dfrac{p^{2}}{2 m}\) where, \(p=\) momentum, \(m=\) mass \(\Rightarrow \dfrac{K_{1}}{K_{2}}=\left(\dfrac{p_{1}}{p_{2}}\right)^{2}\left(\dfrac{m_{2}}{m_{1}}\right)\) Given, \(p_{1}=p_{2}\) \(\Rightarrow \dfrac{K_{1}}{K_{2}}=\dfrac{m_{2}}{m_{1}}\) \(\Rightarrow \dfrac{m_{1}}{m_{2}}=\dfrac{K_{2}}{K_{1}}=\dfrac{9}{16}\)
JEE - 2023
PHXI06:WORK ENERGY AND POWER
355423
Statement A : A light body and a heavy body have same momentum. Then they also have same kinetic energy. Statement B : Kinetic energy does not depend on mass of the body
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both statements are correct.
4 Both Statements are incorrect.
Explanation:
\(K . E=\dfrac{1}{2} m v^{2}=\dfrac{P^{2}}{2 m}\)
PHXI06:WORK ENERGY AND POWER
355424
A particle of mass \(m\) at rest is acted upon by a force \(P\) for a time \(t\). Its kinetic energy after an interval \(t\) is
1 \(\dfrac{P^{2} t^{2}}{m}\)
2 \(\dfrac{P^{2} t^{2}}{2 m}\)
3 \(\dfrac{P^{2} t^{2}}{3 m}\)
4 \(\dfrac{P t}{2 m}\)
Explanation:
Given, force, \(P=m a\) As the kinetic energy, \(K = \frac{1}{2}m{v^2}\) \( = \frac{1}{2}\frac{{{m^2}\left( {{v^2}} \right)}}{m} = \frac{1}{2}\frac{{{m^2}{a^2}{t^2}}}{m}\) \((\because v = at,{\text{ as }}u = 0)\) \( = \frac{{{P^{\,2}}{t^2}}}{{2\,m}}\quad \quad (\because \,\,P = ma)\)
355421
Four particles \(A, B, C, D\) of mass \(\dfrac{m}{2}, m, 2 m, 4 m\), have same momentum, respectively. The particle with maximum kinetic energy is
1 \(C\)
2 \(A\)
3 \(D\)
4 \(B\)
Explanation:
\(K E=\dfrac{p^{2}}{2 m}\) For same momentum \((p), K E \propto \dfrac{1}{m}\) Therefore, the lightest particle will possess maximum kinetic energy. \(\therefore \) A possess maximum kinetic energy. So, correct option is (2).
JEE - 2024
PHXI06:WORK ENERGY AND POWER
355422
Two bodies are having kinetic energies in the ratio \(16: 9\). If they have same linear momentum, the ratio of their masses respectively is
1 \(4: 3\)
2 \(16: 9\)
3 \(3: 4\)
4 \(9: 16\)
Explanation:
Kinetic energy of a body is given by \(K=\dfrac{p^{2}}{2 m}\) where, \(p=\) momentum, \(m=\) mass \(\Rightarrow \dfrac{K_{1}}{K_{2}}=\left(\dfrac{p_{1}}{p_{2}}\right)^{2}\left(\dfrac{m_{2}}{m_{1}}\right)\) Given, \(p_{1}=p_{2}\) \(\Rightarrow \dfrac{K_{1}}{K_{2}}=\dfrac{m_{2}}{m_{1}}\) \(\Rightarrow \dfrac{m_{1}}{m_{2}}=\dfrac{K_{2}}{K_{1}}=\dfrac{9}{16}\)
JEE - 2023
PHXI06:WORK ENERGY AND POWER
355423
Statement A : A light body and a heavy body have same momentum. Then they also have same kinetic energy. Statement B : Kinetic energy does not depend on mass of the body
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both statements are correct.
4 Both Statements are incorrect.
Explanation:
\(K . E=\dfrac{1}{2} m v^{2}=\dfrac{P^{2}}{2 m}\)
PHXI06:WORK ENERGY AND POWER
355424
A particle of mass \(m\) at rest is acted upon by a force \(P\) for a time \(t\). Its kinetic energy after an interval \(t\) is
1 \(\dfrac{P^{2} t^{2}}{m}\)
2 \(\dfrac{P^{2} t^{2}}{2 m}\)
3 \(\dfrac{P^{2} t^{2}}{3 m}\)
4 \(\dfrac{P t}{2 m}\)
Explanation:
Given, force, \(P=m a\) As the kinetic energy, \(K = \frac{1}{2}m{v^2}\) \( = \frac{1}{2}\frac{{{m^2}\left( {{v^2}} \right)}}{m} = \frac{1}{2}\frac{{{m^2}{a^2}{t^2}}}{m}\) \((\because v = at,{\text{ as }}u = 0)\) \( = \frac{{{P^{\,2}}{t^2}}}{{2\,m}}\quad \quad (\because \,\,P = ma)\)
355421
Four particles \(A, B, C, D\) of mass \(\dfrac{m}{2}, m, 2 m, 4 m\), have same momentum, respectively. The particle with maximum kinetic energy is
1 \(C\)
2 \(A\)
3 \(D\)
4 \(B\)
Explanation:
\(K E=\dfrac{p^{2}}{2 m}\) For same momentum \((p), K E \propto \dfrac{1}{m}\) Therefore, the lightest particle will possess maximum kinetic energy. \(\therefore \) A possess maximum kinetic energy. So, correct option is (2).
JEE - 2024
PHXI06:WORK ENERGY AND POWER
355422
Two bodies are having kinetic energies in the ratio \(16: 9\). If they have same linear momentum, the ratio of their masses respectively is
1 \(4: 3\)
2 \(16: 9\)
3 \(3: 4\)
4 \(9: 16\)
Explanation:
Kinetic energy of a body is given by \(K=\dfrac{p^{2}}{2 m}\) where, \(p=\) momentum, \(m=\) mass \(\Rightarrow \dfrac{K_{1}}{K_{2}}=\left(\dfrac{p_{1}}{p_{2}}\right)^{2}\left(\dfrac{m_{2}}{m_{1}}\right)\) Given, \(p_{1}=p_{2}\) \(\Rightarrow \dfrac{K_{1}}{K_{2}}=\dfrac{m_{2}}{m_{1}}\) \(\Rightarrow \dfrac{m_{1}}{m_{2}}=\dfrac{K_{2}}{K_{1}}=\dfrac{9}{16}\)
JEE - 2023
PHXI06:WORK ENERGY AND POWER
355423
Statement A : A light body and a heavy body have same momentum. Then they also have same kinetic energy. Statement B : Kinetic energy does not depend on mass of the body
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both statements are correct.
4 Both Statements are incorrect.
Explanation:
\(K . E=\dfrac{1}{2} m v^{2}=\dfrac{P^{2}}{2 m}\)
PHXI06:WORK ENERGY AND POWER
355424
A particle of mass \(m\) at rest is acted upon by a force \(P\) for a time \(t\). Its kinetic energy after an interval \(t\) is
1 \(\dfrac{P^{2} t^{2}}{m}\)
2 \(\dfrac{P^{2} t^{2}}{2 m}\)
3 \(\dfrac{P^{2} t^{2}}{3 m}\)
4 \(\dfrac{P t}{2 m}\)
Explanation:
Given, force, \(P=m a\) As the kinetic energy, \(K = \frac{1}{2}m{v^2}\) \( = \frac{1}{2}\frac{{{m^2}\left( {{v^2}} \right)}}{m} = \frac{1}{2}\frac{{{m^2}{a^2}{t^2}}}{m}\) \((\because v = at,{\text{ as }}u = 0)\) \( = \frac{{{P^{\,2}}{t^2}}}{{2\,m}}\quad \quad (\because \,\,P = ma)\)
355421
Four particles \(A, B, C, D\) of mass \(\dfrac{m}{2}, m, 2 m, 4 m\), have same momentum, respectively. The particle with maximum kinetic energy is
1 \(C\)
2 \(A\)
3 \(D\)
4 \(B\)
Explanation:
\(K E=\dfrac{p^{2}}{2 m}\) For same momentum \((p), K E \propto \dfrac{1}{m}\) Therefore, the lightest particle will possess maximum kinetic energy. \(\therefore \) A possess maximum kinetic energy. So, correct option is (2).
JEE - 2024
PHXI06:WORK ENERGY AND POWER
355422
Two bodies are having kinetic energies in the ratio \(16: 9\). If they have same linear momentum, the ratio of their masses respectively is
1 \(4: 3\)
2 \(16: 9\)
3 \(3: 4\)
4 \(9: 16\)
Explanation:
Kinetic energy of a body is given by \(K=\dfrac{p^{2}}{2 m}\) where, \(p=\) momentum, \(m=\) mass \(\Rightarrow \dfrac{K_{1}}{K_{2}}=\left(\dfrac{p_{1}}{p_{2}}\right)^{2}\left(\dfrac{m_{2}}{m_{1}}\right)\) Given, \(p_{1}=p_{2}\) \(\Rightarrow \dfrac{K_{1}}{K_{2}}=\dfrac{m_{2}}{m_{1}}\) \(\Rightarrow \dfrac{m_{1}}{m_{2}}=\dfrac{K_{2}}{K_{1}}=\dfrac{9}{16}\)
JEE - 2023
PHXI06:WORK ENERGY AND POWER
355423
Statement A : A light body and a heavy body have same momentum. Then they also have same kinetic energy. Statement B : Kinetic energy does not depend on mass of the body
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both statements are correct.
4 Both Statements are incorrect.
Explanation:
\(K . E=\dfrac{1}{2} m v^{2}=\dfrac{P^{2}}{2 m}\)
PHXI06:WORK ENERGY AND POWER
355424
A particle of mass \(m\) at rest is acted upon by a force \(P\) for a time \(t\). Its kinetic energy after an interval \(t\) is
1 \(\dfrac{P^{2} t^{2}}{m}\)
2 \(\dfrac{P^{2} t^{2}}{2 m}\)
3 \(\dfrac{P^{2} t^{2}}{3 m}\)
4 \(\dfrac{P t}{2 m}\)
Explanation:
Given, force, \(P=m a\) As the kinetic energy, \(K = \frac{1}{2}m{v^2}\) \( = \frac{1}{2}\frac{{{m^2}\left( {{v^2}} \right)}}{m} = \frac{1}{2}\frac{{{m^2}{a^2}{t^2}}}{m}\) \((\because v = at,{\text{ as }}u = 0)\) \( = \frac{{{P^{\,2}}{t^2}}}{{2\,m}}\quad \quad (\because \,\,P = ma)\)
