NEET Test Series from KOTA - 10 Papers In MS WORD
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PHXI08:GRAVITATION
359880
Two bodies of massess \(M\) and \(4 M\) are placed at a distance \(r\). The gravitational potential at a point on the line joining, where the gravitional field is zero, is
1 Zero
2 \(\dfrac{-4 G M}{r}\)
3 \(\dfrac{-6 G M}{r}\)
4 \(\dfrac{-9 G M}{r}\)
Explanation:
Let gravitational field is zero at a distance \(x\) from the mass \(M\). \(\begin{aligned}& \dfrac{G M}{x^{2}}=\dfrac{G(4 M)}{(r-x)^{2}} \\& \Rightarrow 4 x^{2}=(r-x)^{2} \\& 2 x=r-x \Rightarrow x=\dfrac{r}{3}\end{aligned}\) The potential at that point is \(\begin{aligned}& \therefore V_{p}=-\dfrac{G M}{x}-\dfrac{G(4 M)}{r-x} \\& =-\dfrac{3 G M}{r}-\dfrac{6 G M}{r}=-\dfrac{9 G M}{r}\end{aligned}\)
PHXI08:GRAVITATION
359881
Assertion : Gravitational potential inside a charged spherical shell is zero. Reason : Gravitational field and potential are related by \(E=-\dfrac{d V}{d r}\)
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 the Reason is correct.
Explanation:
Gravitational potential inside a charged spherical shell is non zero. \(E=\dfrac{-d V}{d r}\) so option (4) is correct.
PHXI08:GRAVITATION
359882
In some region, the gravitational field is zero. The gravitational potential in this region
1 Must be variable
2 Must be constant
3 Can not be zero
4 Must be zero
Explanation:
\(I = \frac{{dU}}{{dr}} = 0 \Rightarrow U\) is constant. So correct option is (2)
PHXI08:GRAVITATION
359883
The force of gravitation is
1 Conservation
2 Repulsive
3 Non-conservative
4 Electrostatic
Explanation:
Work done by the gravitational force is independent of path followed. It is conservative in nature.
359880
Two bodies of massess \(M\) and \(4 M\) are placed at a distance \(r\). The gravitational potential at a point on the line joining, where the gravitional field is zero, is
1 Zero
2 \(\dfrac{-4 G M}{r}\)
3 \(\dfrac{-6 G M}{r}\)
4 \(\dfrac{-9 G M}{r}\)
Explanation:
Let gravitational field is zero at a distance \(x\) from the mass \(M\). \(\begin{aligned}& \dfrac{G M}{x^{2}}=\dfrac{G(4 M)}{(r-x)^{2}} \\& \Rightarrow 4 x^{2}=(r-x)^{2} \\& 2 x=r-x \Rightarrow x=\dfrac{r}{3}\end{aligned}\) The potential at that point is \(\begin{aligned}& \therefore V_{p}=-\dfrac{G M}{x}-\dfrac{G(4 M)}{r-x} \\& =-\dfrac{3 G M}{r}-\dfrac{6 G M}{r}=-\dfrac{9 G M}{r}\end{aligned}\)
PHXI08:GRAVITATION
359881
Assertion : Gravitational potential inside a charged spherical shell is zero. Reason : Gravitational field and potential are related by \(E=-\dfrac{d V}{d r}\)
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 the Reason is correct.
Explanation:
Gravitational potential inside a charged spherical shell is non zero. \(E=\dfrac{-d V}{d r}\) so option (4) is correct.
PHXI08:GRAVITATION
359882
In some region, the gravitational field is zero. The gravitational potential in this region
1 Must be variable
2 Must be constant
3 Can not be zero
4 Must be zero
Explanation:
\(I = \frac{{dU}}{{dr}} = 0 \Rightarrow U\) is constant. So correct option is (2)
PHXI08:GRAVITATION
359883
The force of gravitation is
1 Conservation
2 Repulsive
3 Non-conservative
4 Electrostatic
Explanation:
Work done by the gravitational force is independent of path followed. It is conservative in nature.
359880
Two bodies of massess \(M\) and \(4 M\) are placed at a distance \(r\). The gravitational potential at a point on the line joining, where the gravitional field is zero, is
1 Zero
2 \(\dfrac{-4 G M}{r}\)
3 \(\dfrac{-6 G M}{r}\)
4 \(\dfrac{-9 G M}{r}\)
Explanation:
Let gravitational field is zero at a distance \(x\) from the mass \(M\). \(\begin{aligned}& \dfrac{G M}{x^{2}}=\dfrac{G(4 M)}{(r-x)^{2}} \\& \Rightarrow 4 x^{2}=(r-x)^{2} \\& 2 x=r-x \Rightarrow x=\dfrac{r}{3}\end{aligned}\) The potential at that point is \(\begin{aligned}& \therefore V_{p}=-\dfrac{G M}{x}-\dfrac{G(4 M)}{r-x} \\& =-\dfrac{3 G M}{r}-\dfrac{6 G M}{r}=-\dfrac{9 G M}{r}\end{aligned}\)
PHXI08:GRAVITATION
359881
Assertion : Gravitational potential inside a charged spherical shell is zero. Reason : Gravitational field and potential are related by \(E=-\dfrac{d V}{d r}\)
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 the Reason is correct.
Explanation:
Gravitational potential inside a charged spherical shell is non zero. \(E=\dfrac{-d V}{d r}\) so option (4) is correct.
PHXI08:GRAVITATION
359882
In some region, the gravitational field is zero. The gravitational potential in this region
1 Must be variable
2 Must be constant
3 Can not be zero
4 Must be zero
Explanation:
\(I = \frac{{dU}}{{dr}} = 0 \Rightarrow U\) is constant. So correct option is (2)
PHXI08:GRAVITATION
359883
The force of gravitation is
1 Conservation
2 Repulsive
3 Non-conservative
4 Electrostatic
Explanation:
Work done by the gravitational force is independent of path followed. It is conservative in nature.
359880
Two bodies of massess \(M\) and \(4 M\) are placed at a distance \(r\). The gravitational potential at a point on the line joining, where the gravitional field is zero, is
1 Zero
2 \(\dfrac{-4 G M}{r}\)
3 \(\dfrac{-6 G M}{r}\)
4 \(\dfrac{-9 G M}{r}\)
Explanation:
Let gravitational field is zero at a distance \(x\) from the mass \(M\). \(\begin{aligned}& \dfrac{G M}{x^{2}}=\dfrac{G(4 M)}{(r-x)^{2}} \\& \Rightarrow 4 x^{2}=(r-x)^{2} \\& 2 x=r-x \Rightarrow x=\dfrac{r}{3}\end{aligned}\) The potential at that point is \(\begin{aligned}& \therefore V_{p}=-\dfrac{G M}{x}-\dfrac{G(4 M)}{r-x} \\& =-\dfrac{3 G M}{r}-\dfrac{6 G M}{r}=-\dfrac{9 G M}{r}\end{aligned}\)
PHXI08:GRAVITATION
359881
Assertion : Gravitational potential inside a charged spherical shell is zero. Reason : Gravitational field and potential are related by \(E=-\dfrac{d V}{d r}\)
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 the Reason is correct.
Explanation:
Gravitational potential inside a charged spherical shell is non zero. \(E=\dfrac{-d V}{d r}\) so option (4) is correct.
PHXI08:GRAVITATION
359882
In some region, the gravitational field is zero. The gravitational potential in this region
1 Must be variable
2 Must be constant
3 Can not be zero
4 Must be zero
Explanation:
\(I = \frac{{dU}}{{dr}} = 0 \Rightarrow U\) is constant. So correct option is (2)
PHXI08:GRAVITATION
359883
The force of gravitation is
1 Conservation
2 Repulsive
3 Non-conservative
4 Electrostatic
Explanation:
Work done by the gravitational force is independent of path followed. It is conservative in nature.
