163808
Four holes of radius \(R\) are cut from a thin square plate of side \(4 R\) and mass \(M\). The moment of intertia of the remaining portion about \(z\)-axis is :
\(M=\) Mass of the square plate before cutting the holes Mass of one hole, \( \mathrm{m}=\left(\frac{\mathrm{M}}{16 \mathrm{R}^2}\right) \pi \mathrm{R}^2=\frac{\pi \mathrm{M}}{16} \) \(\therefore \quad\) Moment of inertia of the remaining portion \( I=I_{\text {square }}-4 I_{\text {hole }} \) \( \begin{aligned} \frac{M}{12}\left(16 R^2+16 R^2\right)-4 } \) \( =\frac{8}{3} M R^2-10 m R^2 \) \( =\left(\frac{8}{3}-\frac{10 \pi}{16}\right) M R^2 \end{aligned} \)
Modified (NLI Expert)
4 RBTS PAPER
163809
Two bodies of mass \(10 \mathrm{~kg}\) and \(2 \mathrm{~kg}\) are moving with velocities \(2 \hat{i}-7 \hat{j}+3 \hat{k}\) and \(-10 \hat{i}+35 \hat{j}-3 \hat{k} \mathrm{~m} / \mathrm{s}\) respectively. The velocities of their centre of mass is
163810
For which of the following does the centre of mass lie outside the body?
1 A pencil
2 A shotput
3 A dice
4 A bangle
Explanation:
A bangle is in the form of a ring as shown in the adjacent diagram. The centre of mass lies at the centre, which is outside the body (boundary)
NCERT-XI- I -96
4 RBTS PAPER
163811
Which of the following points is the likely position of the centre of mass of the system shown in figure?
1 \(A\)
2 \(\mathrm{B}\)
3 \(\mathrm{C}\)
4 \(D\)
Explanation:
Centre of mass of a system lies towards the part of the system, having bigger mass. In the above diagram, lower part is heavier, hence \(\mathrm{CM}\) of the system lies below the horizontal diameter.
NCERT-XI- I -97
4 RBTS PAPER
163812
Assertion : For a system of particles under central force field, the total angular momentum is conserved. Reason : The torque acting on such a system is zero.
1 Assertion is correct, reason is correct; reason is a correct explanation for assertion.
2 Assertion is correct, reason is correct; reason is not a correct explanation for assertion.
3 Assertion is correct, reason is incorrect.
4 Assertion is incorrect, reason is correct.
Explanation:
Assertion is correct, reason is correct; reason is a correct explanation for assertion.
163808
Four holes of radius \(R\) are cut from a thin square plate of side \(4 R\) and mass \(M\). The moment of intertia of the remaining portion about \(z\)-axis is :
\(M=\) Mass of the square plate before cutting the holes Mass of one hole, \( \mathrm{m}=\left(\frac{\mathrm{M}}{16 \mathrm{R}^2}\right) \pi \mathrm{R}^2=\frac{\pi \mathrm{M}}{16} \) \(\therefore \quad\) Moment of inertia of the remaining portion \( I=I_{\text {square }}-4 I_{\text {hole }} \) \( \begin{aligned} \frac{M}{12}\left(16 R^2+16 R^2\right)-4 } \) \( =\frac{8}{3} M R^2-10 m R^2 \) \( =\left(\frac{8}{3}-\frac{10 \pi}{16}\right) M R^2 \end{aligned} \)
Modified (NLI Expert)
4 RBTS PAPER
163809
Two bodies of mass \(10 \mathrm{~kg}\) and \(2 \mathrm{~kg}\) are moving with velocities \(2 \hat{i}-7 \hat{j}+3 \hat{k}\) and \(-10 \hat{i}+35 \hat{j}-3 \hat{k} \mathrm{~m} / \mathrm{s}\) respectively. The velocities of their centre of mass is
163810
For which of the following does the centre of mass lie outside the body?
1 A pencil
2 A shotput
3 A dice
4 A bangle
Explanation:
A bangle is in the form of a ring as shown in the adjacent diagram. The centre of mass lies at the centre, which is outside the body (boundary)
NCERT-XI- I -96
4 RBTS PAPER
163811
Which of the following points is the likely position of the centre of mass of the system shown in figure?
1 \(A\)
2 \(\mathrm{B}\)
3 \(\mathrm{C}\)
4 \(D\)
Explanation:
Centre of mass of a system lies towards the part of the system, having bigger mass. In the above diagram, lower part is heavier, hence \(\mathrm{CM}\) of the system lies below the horizontal diameter.
NCERT-XI- I -97
4 RBTS PAPER
163812
Assertion : For a system of particles under central force field, the total angular momentum is conserved. Reason : The torque acting on such a system is zero.
1 Assertion is correct, reason is correct; reason is a correct explanation for assertion.
2 Assertion is correct, reason is correct; reason is not a correct explanation for assertion.
3 Assertion is correct, reason is incorrect.
4 Assertion is incorrect, reason is correct.
Explanation:
Assertion is correct, reason is correct; reason is a correct explanation for assertion.
163808
Four holes of radius \(R\) are cut from a thin square plate of side \(4 R\) and mass \(M\). The moment of intertia of the remaining portion about \(z\)-axis is :
\(M=\) Mass of the square plate before cutting the holes Mass of one hole, \( \mathrm{m}=\left(\frac{\mathrm{M}}{16 \mathrm{R}^2}\right) \pi \mathrm{R}^2=\frac{\pi \mathrm{M}}{16} \) \(\therefore \quad\) Moment of inertia of the remaining portion \( I=I_{\text {square }}-4 I_{\text {hole }} \) \( \begin{aligned} \frac{M}{12}\left(16 R^2+16 R^2\right)-4 } \) \( =\frac{8}{3} M R^2-10 m R^2 \) \( =\left(\frac{8}{3}-\frac{10 \pi}{16}\right) M R^2 \end{aligned} \)
Modified (NLI Expert)
4 RBTS PAPER
163809
Two bodies of mass \(10 \mathrm{~kg}\) and \(2 \mathrm{~kg}\) are moving with velocities \(2 \hat{i}-7 \hat{j}+3 \hat{k}\) and \(-10 \hat{i}+35 \hat{j}-3 \hat{k} \mathrm{~m} / \mathrm{s}\) respectively. The velocities of their centre of mass is
163810
For which of the following does the centre of mass lie outside the body?
1 A pencil
2 A shotput
3 A dice
4 A bangle
Explanation:
A bangle is in the form of a ring as shown in the adjacent diagram. The centre of mass lies at the centre, which is outside the body (boundary)
NCERT-XI- I -96
4 RBTS PAPER
163811
Which of the following points is the likely position of the centre of mass of the system shown in figure?
1 \(A\)
2 \(\mathrm{B}\)
3 \(\mathrm{C}\)
4 \(D\)
Explanation:
Centre of mass of a system lies towards the part of the system, having bigger mass. In the above diagram, lower part is heavier, hence \(\mathrm{CM}\) of the system lies below the horizontal diameter.
NCERT-XI- I -97
4 RBTS PAPER
163812
Assertion : For a system of particles under central force field, the total angular momentum is conserved. Reason : The torque acting on such a system is zero.
1 Assertion is correct, reason is correct; reason is a correct explanation for assertion.
2 Assertion is correct, reason is correct; reason is not a correct explanation for assertion.
3 Assertion is correct, reason is incorrect.
4 Assertion is incorrect, reason is correct.
Explanation:
Assertion is correct, reason is correct; reason is a correct explanation for assertion.
163808
Four holes of radius \(R\) are cut from a thin square plate of side \(4 R\) and mass \(M\). The moment of intertia of the remaining portion about \(z\)-axis is :
\(M=\) Mass of the square plate before cutting the holes Mass of one hole, \( \mathrm{m}=\left(\frac{\mathrm{M}}{16 \mathrm{R}^2}\right) \pi \mathrm{R}^2=\frac{\pi \mathrm{M}}{16} \) \(\therefore \quad\) Moment of inertia of the remaining portion \( I=I_{\text {square }}-4 I_{\text {hole }} \) \( \begin{aligned} \frac{M}{12}\left(16 R^2+16 R^2\right)-4 } \) \( =\frac{8}{3} M R^2-10 m R^2 \) \( =\left(\frac{8}{3}-\frac{10 \pi}{16}\right) M R^2 \end{aligned} \)
Modified (NLI Expert)
4 RBTS PAPER
163809
Two bodies of mass \(10 \mathrm{~kg}\) and \(2 \mathrm{~kg}\) are moving with velocities \(2 \hat{i}-7 \hat{j}+3 \hat{k}\) and \(-10 \hat{i}+35 \hat{j}-3 \hat{k} \mathrm{~m} / \mathrm{s}\) respectively. The velocities of their centre of mass is
163810
For which of the following does the centre of mass lie outside the body?
1 A pencil
2 A shotput
3 A dice
4 A bangle
Explanation:
A bangle is in the form of a ring as shown in the adjacent diagram. The centre of mass lies at the centre, which is outside the body (boundary)
NCERT-XI- I -96
4 RBTS PAPER
163811
Which of the following points is the likely position of the centre of mass of the system shown in figure?
1 \(A\)
2 \(\mathrm{B}\)
3 \(\mathrm{C}\)
4 \(D\)
Explanation:
Centre of mass of a system lies towards the part of the system, having bigger mass. In the above diagram, lower part is heavier, hence \(\mathrm{CM}\) of the system lies below the horizontal diameter.
NCERT-XI- I -97
4 RBTS PAPER
163812
Assertion : For a system of particles under central force field, the total angular momentum is conserved. Reason : The torque acting on such a system is zero.
1 Assertion is correct, reason is correct; reason is a correct explanation for assertion.
2 Assertion is correct, reason is correct; reason is not a correct explanation for assertion.
3 Assertion is correct, reason is incorrect.
4 Assertion is incorrect, reason is correct.
Explanation:
Assertion is correct, reason is correct; reason is a correct explanation for assertion.
163808
Four holes of radius \(R\) are cut from a thin square plate of side \(4 R\) and mass \(M\). The moment of intertia of the remaining portion about \(z\)-axis is :
\(M=\) Mass of the square plate before cutting the holes Mass of one hole, \( \mathrm{m}=\left(\frac{\mathrm{M}}{16 \mathrm{R}^2}\right) \pi \mathrm{R}^2=\frac{\pi \mathrm{M}}{16} \) \(\therefore \quad\) Moment of inertia of the remaining portion \( I=I_{\text {square }}-4 I_{\text {hole }} \) \( \begin{aligned} \frac{M}{12}\left(16 R^2+16 R^2\right)-4 } \) \( =\frac{8}{3} M R^2-10 m R^2 \) \( =\left(\frac{8}{3}-\frac{10 \pi}{16}\right) M R^2 \end{aligned} \)
Modified (NLI Expert)
4 RBTS PAPER
163809
Two bodies of mass \(10 \mathrm{~kg}\) and \(2 \mathrm{~kg}\) are moving with velocities \(2 \hat{i}-7 \hat{j}+3 \hat{k}\) and \(-10 \hat{i}+35 \hat{j}-3 \hat{k} \mathrm{~m} / \mathrm{s}\) respectively. The velocities of their centre of mass is
163810
For which of the following does the centre of mass lie outside the body?
1 A pencil
2 A shotput
3 A dice
4 A bangle
Explanation:
A bangle is in the form of a ring as shown in the adjacent diagram. The centre of mass lies at the centre, which is outside the body (boundary)
NCERT-XI- I -96
4 RBTS PAPER
163811
Which of the following points is the likely position of the centre of mass of the system shown in figure?
1 \(A\)
2 \(\mathrm{B}\)
3 \(\mathrm{C}\)
4 \(D\)
Explanation:
Centre of mass of a system lies towards the part of the system, having bigger mass. In the above diagram, lower part is heavier, hence \(\mathrm{CM}\) of the system lies below the horizontal diameter.
NCERT-XI- I -97
4 RBTS PAPER
163812
Assertion : For a system of particles under central force field, the total angular momentum is conserved. Reason : The torque acting on such a system is zero.
1 Assertion is correct, reason is correct; reason is a correct explanation for assertion.
2 Assertion is correct, reason is correct; reason is not a correct explanation for assertion.
3 Assertion is correct, reason is incorrect.
4 Assertion is incorrect, reason is correct.
Explanation:
Assertion is correct, reason is correct; reason is a correct explanation for assertion.
