266276
A small disc of radius 2 cm is cut from a disc of radius 6 cm . If the distance between their centres is 3.2 cm , what is the shift in the centre of mass of the disc:
1 0.4 cm
2 2.4 cm
3 1.8 cm
4 1.2 cm
Explanation:
a The situation can be shown as: Let radius of complete disc is a and that of small disc is b. also let centre of mass now shifts to \(\mathrm{O}_2\) at a distance \(\mathrm{x}_2\) from original centre. The position of new centre of mass is given by \(X_{C M}=\frac{-\sigma \pi b^2 x_1}{a \pi a^2-a \pi b^2} \) Here, \(a=6 \mathrm{~cm}, b=2 \mathrm{~cm}, x_1=3.2 \mathrm{~cm}\) Hence, \(X_{\text {cu }}=\frac{-\sigma \times \pi(2)^2 \times 3.2}{\sigma \times \pi \times(6)^2-\sigma \times \pi \times(2)^2}\) \[ =\frac{12.8 \pi}{32 \pi}=-0.4 \mathrm{~cm} \]
**NLIExpert**
TEST SERIES (PHYSICS FST)
266277
Statement I: The phase difference between displacement and acceleration of a particle in SHM is \(\pi \mathrm{rad}\). Statement II : The circular motion of a particle with constant speed is both periodic and SHM.
1 Statement I is correct and Statement II is incorrect
2 Statement I is incorrect and Statemnet II is correct
3 Both Statement I and II is correct
4 Both Statement I and II is incorrect
Explanation:
a
**NCERT-XI-II.266**
TEST SERIES (PHYSICS FST)
266278
In a region the intensity of an electric field is given by \(\mathbf{E}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) in \(\mathrm{NC}^{-1}\). The electric flux through a surface \(\mathbf{S}=\mathbf{1 0} \hat{\mathbf{k}} \mathrm{m}^2\) in the region is:
266276
A small disc of radius 2 cm is cut from a disc of radius 6 cm . If the distance between their centres is 3.2 cm , what is the shift in the centre of mass of the disc:
1 0.4 cm
2 2.4 cm
3 1.8 cm
4 1.2 cm
Explanation:
a The situation can be shown as: Let radius of complete disc is a and that of small disc is b. also let centre of mass now shifts to \(\mathrm{O}_2\) at a distance \(\mathrm{x}_2\) from original centre. The position of new centre of mass is given by \(X_{C M}=\frac{-\sigma \pi b^2 x_1}{a \pi a^2-a \pi b^2} \) Here, \(a=6 \mathrm{~cm}, b=2 \mathrm{~cm}, x_1=3.2 \mathrm{~cm}\) Hence, \(X_{\text {cu }}=\frac{-\sigma \times \pi(2)^2 \times 3.2}{\sigma \times \pi \times(6)^2-\sigma \times \pi \times(2)^2}\) \[ =\frac{12.8 \pi}{32 \pi}=-0.4 \mathrm{~cm} \]
**NLIExpert**
TEST SERIES (PHYSICS FST)
266277
Statement I: The phase difference between displacement and acceleration of a particle in SHM is \(\pi \mathrm{rad}\). Statement II : The circular motion of a particle with constant speed is both periodic and SHM.
1 Statement I is correct and Statement II is incorrect
2 Statement I is incorrect and Statemnet II is correct
3 Both Statement I and II is correct
4 Both Statement I and II is incorrect
Explanation:
a
**NCERT-XI-II.266**
TEST SERIES (PHYSICS FST)
266278
In a region the intensity of an electric field is given by \(\mathbf{E}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) in \(\mathrm{NC}^{-1}\). The electric flux through a surface \(\mathbf{S}=\mathbf{1 0} \hat{\mathbf{k}} \mathrm{m}^2\) in the region is:
266276
A small disc of radius 2 cm is cut from a disc of radius 6 cm . If the distance between their centres is 3.2 cm , what is the shift in the centre of mass of the disc:
1 0.4 cm
2 2.4 cm
3 1.8 cm
4 1.2 cm
Explanation:
a The situation can be shown as: Let radius of complete disc is a and that of small disc is b. also let centre of mass now shifts to \(\mathrm{O}_2\) at a distance \(\mathrm{x}_2\) from original centre. The position of new centre of mass is given by \(X_{C M}=\frac{-\sigma \pi b^2 x_1}{a \pi a^2-a \pi b^2} \) Here, \(a=6 \mathrm{~cm}, b=2 \mathrm{~cm}, x_1=3.2 \mathrm{~cm}\) Hence, \(X_{\text {cu }}=\frac{-\sigma \times \pi(2)^2 \times 3.2}{\sigma \times \pi \times(6)^2-\sigma \times \pi \times(2)^2}\) \[ =\frac{12.8 \pi}{32 \pi}=-0.4 \mathrm{~cm} \]
**NLIExpert**
TEST SERIES (PHYSICS FST)
266277
Statement I: The phase difference between displacement and acceleration of a particle in SHM is \(\pi \mathrm{rad}\). Statement II : The circular motion of a particle with constant speed is both periodic and SHM.
1 Statement I is correct and Statement II is incorrect
2 Statement I is incorrect and Statemnet II is correct
3 Both Statement I and II is correct
4 Both Statement I and II is incorrect
Explanation:
a
**NCERT-XI-II.266**
TEST SERIES (PHYSICS FST)
266278
In a region the intensity of an electric field is given by \(\mathbf{E}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) in \(\mathrm{NC}^{-1}\). The electric flux through a surface \(\mathbf{S}=\mathbf{1 0} \hat{\mathbf{k}} \mathrm{m}^2\) in the region is:
266276
A small disc of radius 2 cm is cut from a disc of radius 6 cm . If the distance between their centres is 3.2 cm , what is the shift in the centre of mass of the disc:
1 0.4 cm
2 2.4 cm
3 1.8 cm
4 1.2 cm
Explanation:
a The situation can be shown as: Let radius of complete disc is a and that of small disc is b. also let centre of mass now shifts to \(\mathrm{O}_2\) at a distance \(\mathrm{x}_2\) from original centre. The position of new centre of mass is given by \(X_{C M}=\frac{-\sigma \pi b^2 x_1}{a \pi a^2-a \pi b^2} \) Here, \(a=6 \mathrm{~cm}, b=2 \mathrm{~cm}, x_1=3.2 \mathrm{~cm}\) Hence, \(X_{\text {cu }}=\frac{-\sigma \times \pi(2)^2 \times 3.2}{\sigma \times \pi \times(6)^2-\sigma \times \pi \times(2)^2}\) \[ =\frac{12.8 \pi}{32 \pi}=-0.4 \mathrm{~cm} \]
**NLIExpert**
TEST SERIES (PHYSICS FST)
266277
Statement I: The phase difference between displacement and acceleration of a particle in SHM is \(\pi \mathrm{rad}\). Statement II : The circular motion of a particle with constant speed is both periodic and SHM.
1 Statement I is correct and Statement II is incorrect
2 Statement I is incorrect and Statemnet II is correct
3 Both Statement I and II is correct
4 Both Statement I and II is incorrect
Explanation:
a
**NCERT-XI-II.266**
TEST SERIES (PHYSICS FST)
266278
In a region the intensity of an electric field is given by \(\mathbf{E}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) in \(\mathrm{NC}^{-1}\). The electric flux through a surface \(\mathbf{S}=\mathbf{1 0} \hat{\mathbf{k}} \mathrm{m}^2\) in the region is:
