366187
A particle is made to move in circular path with varying speed. Which of the following is correct? (i) Direction of \(\bar{L}\) is constant (ii) Acceleration is neither along the tangent nor along the radius
1 Both (i) and (ii) are incorrect
2 Both (i) and (ii) are correct
3 Only (i) is correct
4 Only (ii) is correct
Explanation:
As speed changes \(\vec{L}=\vec{r} \times m \vec{v}\) The direction of \(\vec{L}\) remains same whereas its magnitude changes.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366188
A particle of mass m moves in the \(xy\)-plane with a velocity of \(\vec{v}=v_{x} \hat{i}+v_{y} \hat{j}\). When its position vector is \(\vec{r}=x \hat{i}+y \hat{j}\), the angular momentum of the particle about the origin is
1 \(-m\left(x v_{y}+y v_{x}\right) \hat{k}\)
2 \(m\left(x v_{y}+y v_{x}\right) \hat{k}\)
3 \(m\left(x v_{y}-y v_{x}\right) \hat{k}\)
4 \(m\left(y v_{x}-x v_{y}\right) \hat{k}\)
Explanation:
We use \(\vec{L}=\vec{r} \times \vec{p}\) \(\begin{aligned}& \vec{L}=\left|\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \\x & y & 0 \\m v_{x} & m v_{y} & 0\end{array}\right| \\& =\hat{i}(0-0)-\hat{j}(0-0)+\hat{k}\left(m x v_{y}-m y v_{x}\right) \\& \vec{L}=m\left(x v_{y}-y v_{x}\right) \hat{k}\end{aligned}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366189
Angular momentum \(L\) is given by \(L=p \cdot r\). The variation of \(\log L\) and \(\log p\) is shown by
1 I
2 II
3 III
4 IV
Explanation:
Angular momentum, \(L=r p\) Taking \(\log\) on both sides, we get \(\log _{e} L=\log _{e} p+\log _{e} r\)
\(\therefore\) The graph is drawn between \(\log _{e} L\) and \(\log _{e} p\) is a straight line, which is not pass through the origin.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366190
Find the torque of force \(F=-3 \hat{i}+2 \hat{j}+\hat{k}\) acting at the point \(r=8 \hat{i}+2 \hat{j}+3 \hat{k}\).
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PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366187
A particle is made to move in circular path with varying speed. Which of the following is correct? (i) Direction of \(\bar{L}\) is constant (ii) Acceleration is neither along the tangent nor along the radius
1 Both (i) and (ii) are incorrect
2 Both (i) and (ii) are correct
3 Only (i) is correct
4 Only (ii) is correct
Explanation:
As speed changes \(\vec{L}=\vec{r} \times m \vec{v}\) The direction of \(\vec{L}\) remains same whereas its magnitude changes.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366188
A particle of mass m moves in the \(xy\)-plane with a velocity of \(\vec{v}=v_{x} \hat{i}+v_{y} \hat{j}\). When its position vector is \(\vec{r}=x \hat{i}+y \hat{j}\), the angular momentum of the particle about the origin is
1 \(-m\left(x v_{y}+y v_{x}\right) \hat{k}\)
2 \(m\left(x v_{y}+y v_{x}\right) \hat{k}\)
3 \(m\left(x v_{y}-y v_{x}\right) \hat{k}\)
4 \(m\left(y v_{x}-x v_{y}\right) \hat{k}\)
Explanation:
We use \(\vec{L}=\vec{r} \times \vec{p}\) \(\begin{aligned}& \vec{L}=\left|\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \\x & y & 0 \\m v_{x} & m v_{y} & 0\end{array}\right| \\& =\hat{i}(0-0)-\hat{j}(0-0)+\hat{k}\left(m x v_{y}-m y v_{x}\right) \\& \vec{L}=m\left(x v_{y}-y v_{x}\right) \hat{k}\end{aligned}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366189
Angular momentum \(L\) is given by \(L=p \cdot r\). The variation of \(\log L\) and \(\log p\) is shown by
1 I
2 II
3 III
4 IV
Explanation:
Angular momentum, \(L=r p\) Taking \(\log\) on both sides, we get \(\log _{e} L=\log _{e} p+\log _{e} r\)
\(\therefore\) The graph is drawn between \(\log _{e} L\) and \(\log _{e} p\) is a straight line, which is not pass through the origin.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366190
Find the torque of force \(F=-3 \hat{i}+2 \hat{j}+\hat{k}\) acting at the point \(r=8 \hat{i}+2 \hat{j}+3 \hat{k}\).
366187
A particle is made to move in circular path with varying speed. Which of the following is correct? (i) Direction of \(\bar{L}\) is constant (ii) Acceleration is neither along the tangent nor along the radius
1 Both (i) and (ii) are incorrect
2 Both (i) and (ii) are correct
3 Only (i) is correct
4 Only (ii) is correct
Explanation:
As speed changes \(\vec{L}=\vec{r} \times m \vec{v}\) The direction of \(\vec{L}\) remains same whereas its magnitude changes.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366188
A particle of mass m moves in the \(xy\)-plane with a velocity of \(\vec{v}=v_{x} \hat{i}+v_{y} \hat{j}\). When its position vector is \(\vec{r}=x \hat{i}+y \hat{j}\), the angular momentum of the particle about the origin is
1 \(-m\left(x v_{y}+y v_{x}\right) \hat{k}\)
2 \(m\left(x v_{y}+y v_{x}\right) \hat{k}\)
3 \(m\left(x v_{y}-y v_{x}\right) \hat{k}\)
4 \(m\left(y v_{x}-x v_{y}\right) \hat{k}\)
Explanation:
We use \(\vec{L}=\vec{r} \times \vec{p}\) \(\begin{aligned}& \vec{L}=\left|\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \\x & y & 0 \\m v_{x} & m v_{y} & 0\end{array}\right| \\& =\hat{i}(0-0)-\hat{j}(0-0)+\hat{k}\left(m x v_{y}-m y v_{x}\right) \\& \vec{L}=m\left(x v_{y}-y v_{x}\right) \hat{k}\end{aligned}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366189
Angular momentum \(L\) is given by \(L=p \cdot r\). The variation of \(\log L\) and \(\log p\) is shown by
1 I
2 II
3 III
4 IV
Explanation:
Angular momentum, \(L=r p\) Taking \(\log\) on both sides, we get \(\log _{e} L=\log _{e} p+\log _{e} r\)
\(\therefore\) The graph is drawn between \(\log _{e} L\) and \(\log _{e} p\) is a straight line, which is not pass through the origin.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366190
Find the torque of force \(F=-3 \hat{i}+2 \hat{j}+\hat{k}\) acting at the point \(r=8 \hat{i}+2 \hat{j}+3 \hat{k}\).
366187
A particle is made to move in circular path with varying speed. Which of the following is correct? (i) Direction of \(\bar{L}\) is constant (ii) Acceleration is neither along the tangent nor along the radius
1 Both (i) and (ii) are incorrect
2 Both (i) and (ii) are correct
3 Only (i) is correct
4 Only (ii) is correct
Explanation:
As speed changes \(\vec{L}=\vec{r} \times m \vec{v}\) The direction of \(\vec{L}\) remains same whereas its magnitude changes.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366188
A particle of mass m moves in the \(xy\)-plane with a velocity of \(\vec{v}=v_{x} \hat{i}+v_{y} \hat{j}\). When its position vector is \(\vec{r}=x \hat{i}+y \hat{j}\), the angular momentum of the particle about the origin is
1 \(-m\left(x v_{y}+y v_{x}\right) \hat{k}\)
2 \(m\left(x v_{y}+y v_{x}\right) \hat{k}\)
3 \(m\left(x v_{y}-y v_{x}\right) \hat{k}\)
4 \(m\left(y v_{x}-x v_{y}\right) \hat{k}\)
Explanation:
We use \(\vec{L}=\vec{r} \times \vec{p}\) \(\begin{aligned}& \vec{L}=\left|\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \\x & y & 0 \\m v_{x} & m v_{y} & 0\end{array}\right| \\& =\hat{i}(0-0)-\hat{j}(0-0)+\hat{k}\left(m x v_{y}-m y v_{x}\right) \\& \vec{L}=m\left(x v_{y}-y v_{x}\right) \hat{k}\end{aligned}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366189
Angular momentum \(L\) is given by \(L=p \cdot r\). The variation of \(\log L\) and \(\log p\) is shown by
1 I
2 II
3 III
4 IV
Explanation:
Angular momentum, \(L=r p\) Taking \(\log\) on both sides, we get \(\log _{e} L=\log _{e} p+\log _{e} r\)
\(\therefore\) The graph is drawn between \(\log _{e} L\) and \(\log _{e} p\) is a straight line, which is not pass through the origin.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366190
Find the torque of force \(F=-3 \hat{i}+2 \hat{j}+\hat{k}\) acting at the point \(r=8 \hat{i}+2 \hat{j}+3 \hat{k}\).
