355506
Assertion : The instantaneous power of an agent is measured as the dot product of instantaneous velocity and the force acting on it at that instant. Reason : The unit of instantaneous power is watt.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The rate of doing work is called power. \(\Rightarrow P=\dfrac{W}{t}\), If \(\Delta W\) is the small amount of work done in a small time interval ( \(\Delta t\) ), then instantaneous power is defined as \(P=\lim _{\Delta t \rightarrow 0} \dfrac{\Delta W}{\Delta t}=\dfrac{d W}{d t}\), \(=\dfrac{\vec{F} \cdot d \vec{s}}{d t}=\vec{F} \cdot \vec{v}\) \(\Rightarrow\) Assertion is correct But it is a separate fact that the unit of power is Watt. So correct option is (2)
PHXI06:WORK ENERGY AND POWER
355507
A body of mass \(m\) accelerates uniformly from rest to \(v_{1}\) in time \(t_{1}\). As a function of time \(\mathrm{t}\), the instantaneous power delivered to the body is
1 \(\dfrac{m v_{1}^{2} t}{t_{1}^{2}}\)
2 \(\dfrac{m v_{1}^{2} t}{t_{1}}\)
3 \(\dfrac{m v_{1} t}{t_{1}}\)
4 \(\dfrac{m v_{1} t^{2}}{t_{1}}\)
Explanation:
\(P=\vec{F} \cdot \vec{v}=m a \times a t=m a^{2} t[\) as \(\mathrm{u}=0]\) \(=m\left(\dfrac{v_{1}}{t_{1}}\right)^{2} t=\dfrac{m v_{1}^{2}}{t_{1}^{2}} \times t \quad\left[a=v_{1} / t_{1}\right]\)
PHXI06:WORK ENERGY AND POWER
355508
A particle of mass \(m\) is moving in a circular path of constant radius \(r\) such that centripetal acceleration is varying with time \(t\) as \(k^{2} r t^{2}\), where \(k\) is constant. The power delivered to the particle by the force acting on it is
355509
A force \((4 \hat{i}+\hat{j}-2 \hat{k}) N\) acting on a body maintains its velocity at \((2\hat i + 2\hat j + 3\hat k)m{s^{ - 1}}\). The power exerted is
355506
Assertion : The instantaneous power of an agent is measured as the dot product of instantaneous velocity and the force acting on it at that instant. Reason : The unit of instantaneous power is watt.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The rate of doing work is called power. \(\Rightarrow P=\dfrac{W}{t}\), If \(\Delta W\) is the small amount of work done in a small time interval ( \(\Delta t\) ), then instantaneous power is defined as \(P=\lim _{\Delta t \rightarrow 0} \dfrac{\Delta W}{\Delta t}=\dfrac{d W}{d t}\), \(=\dfrac{\vec{F} \cdot d \vec{s}}{d t}=\vec{F} \cdot \vec{v}\) \(\Rightarrow\) Assertion is correct But it is a separate fact that the unit of power is Watt. So correct option is (2)
PHXI06:WORK ENERGY AND POWER
355507
A body of mass \(m\) accelerates uniformly from rest to \(v_{1}\) in time \(t_{1}\). As a function of time \(\mathrm{t}\), the instantaneous power delivered to the body is
1 \(\dfrac{m v_{1}^{2} t}{t_{1}^{2}}\)
2 \(\dfrac{m v_{1}^{2} t}{t_{1}}\)
3 \(\dfrac{m v_{1} t}{t_{1}}\)
4 \(\dfrac{m v_{1} t^{2}}{t_{1}}\)
Explanation:
\(P=\vec{F} \cdot \vec{v}=m a \times a t=m a^{2} t[\) as \(\mathrm{u}=0]\) \(=m\left(\dfrac{v_{1}}{t_{1}}\right)^{2} t=\dfrac{m v_{1}^{2}}{t_{1}^{2}} \times t \quad\left[a=v_{1} / t_{1}\right]\)
PHXI06:WORK ENERGY AND POWER
355508
A particle of mass \(m\) is moving in a circular path of constant radius \(r\) such that centripetal acceleration is varying with time \(t\) as \(k^{2} r t^{2}\), where \(k\) is constant. The power delivered to the particle by the force acting on it is
355509
A force \((4 \hat{i}+\hat{j}-2 \hat{k}) N\) acting on a body maintains its velocity at \((2\hat i + 2\hat j + 3\hat k)m{s^{ - 1}}\). The power exerted is
355506
Assertion : The instantaneous power of an agent is measured as the dot product of instantaneous velocity and the force acting on it at that instant. Reason : The unit of instantaneous power is watt.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The rate of doing work is called power. \(\Rightarrow P=\dfrac{W}{t}\), If \(\Delta W\) is the small amount of work done in a small time interval ( \(\Delta t\) ), then instantaneous power is defined as \(P=\lim _{\Delta t \rightarrow 0} \dfrac{\Delta W}{\Delta t}=\dfrac{d W}{d t}\), \(=\dfrac{\vec{F} \cdot d \vec{s}}{d t}=\vec{F} \cdot \vec{v}\) \(\Rightarrow\) Assertion is correct But it is a separate fact that the unit of power is Watt. So correct option is (2)
PHXI06:WORK ENERGY AND POWER
355507
A body of mass \(m\) accelerates uniformly from rest to \(v_{1}\) in time \(t_{1}\). As a function of time \(\mathrm{t}\), the instantaneous power delivered to the body is
1 \(\dfrac{m v_{1}^{2} t}{t_{1}^{2}}\)
2 \(\dfrac{m v_{1}^{2} t}{t_{1}}\)
3 \(\dfrac{m v_{1} t}{t_{1}}\)
4 \(\dfrac{m v_{1} t^{2}}{t_{1}}\)
Explanation:
\(P=\vec{F} \cdot \vec{v}=m a \times a t=m a^{2} t[\) as \(\mathrm{u}=0]\) \(=m\left(\dfrac{v_{1}}{t_{1}}\right)^{2} t=\dfrac{m v_{1}^{2}}{t_{1}^{2}} \times t \quad\left[a=v_{1} / t_{1}\right]\)
PHXI06:WORK ENERGY AND POWER
355508
A particle of mass \(m\) is moving in a circular path of constant radius \(r\) such that centripetal acceleration is varying with time \(t\) as \(k^{2} r t^{2}\), where \(k\) is constant. The power delivered to the particle by the force acting on it is
355509
A force \((4 \hat{i}+\hat{j}-2 \hat{k}) N\) acting on a body maintains its velocity at \((2\hat i + 2\hat j + 3\hat k)m{s^{ - 1}}\). The power exerted is
355506
Assertion : The instantaneous power of an agent is measured as the dot product of instantaneous velocity and the force acting on it at that instant. Reason : The unit of instantaneous power is watt.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The rate of doing work is called power. \(\Rightarrow P=\dfrac{W}{t}\), If \(\Delta W\) is the small amount of work done in a small time interval ( \(\Delta t\) ), then instantaneous power is defined as \(P=\lim _{\Delta t \rightarrow 0} \dfrac{\Delta W}{\Delta t}=\dfrac{d W}{d t}\), \(=\dfrac{\vec{F} \cdot d \vec{s}}{d t}=\vec{F} \cdot \vec{v}\) \(\Rightarrow\) Assertion is correct But it is a separate fact that the unit of power is Watt. So correct option is (2)
PHXI06:WORK ENERGY AND POWER
355507
A body of mass \(m\) accelerates uniformly from rest to \(v_{1}\) in time \(t_{1}\). As a function of time \(\mathrm{t}\), the instantaneous power delivered to the body is
1 \(\dfrac{m v_{1}^{2} t}{t_{1}^{2}}\)
2 \(\dfrac{m v_{1}^{2} t}{t_{1}}\)
3 \(\dfrac{m v_{1} t}{t_{1}}\)
4 \(\dfrac{m v_{1} t^{2}}{t_{1}}\)
Explanation:
\(P=\vec{F} \cdot \vec{v}=m a \times a t=m a^{2} t[\) as \(\mathrm{u}=0]\) \(=m\left(\dfrac{v_{1}}{t_{1}}\right)^{2} t=\dfrac{m v_{1}^{2}}{t_{1}^{2}} \times t \quad\left[a=v_{1} / t_{1}\right]\)
PHXI06:WORK ENERGY AND POWER
355508
A particle of mass \(m\) is moving in a circular path of constant radius \(r\) such that centripetal acceleration is varying with time \(t\) as \(k^{2} r t^{2}\), where \(k\) is constant. The power delivered to the particle by the force acting on it is
355509
A force \((4 \hat{i}+\hat{j}-2 \hat{k}) N\) acting on a body maintains its velocity at \((2\hat i + 2\hat j + 3\hat k)m{s^{ - 1}}\). The power exerted is
