Q. No.The arrangement shows two pistons \(P_1,P_2\) with a rigid connecting rod \(C\) so that they can slide together with respect to the two fixed cylinders of cross-sectional areas \(A_1,A_2\) respectively. The two cylinders are connected by means of two pipes to a small cylinder (of area \(A\)) with a piston at the bottom on which is applied a force \(F.\) The interior of the pipes and cylinder is filled with an incompressible oil. Ignore any pressure variations due to gravity. The net force on the two pistons \(P_1, P_2\) is:
1. \(\dfrac{F}{A}(A_1+A_2)\) to right.
2. \(\dfrac{F}{A}(A_1+A_2)\) to left.
3. \(\dfrac{F}{A}(A_2-A_1)\) to right.
4. \(\dfrac{F}{A}(A_2-A_1)\) to left.
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| 1. | \(\dfrac{R}{6t}\) | 2. | \(\dfrac{R}{3t}\) |
| 3. | \(\dfrac{6t}{R}\) | 4. | \(\dfrac{3t}{R}\) |
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1. \(P_A=P_B\)
2. \(P_A-P_B=L\rho a\)
3. \(P_B-P_A=L\rho a\)
4. \(P_A-P_B=L\rho \sqrt{a^2+g^2}\)
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1. \(\rho Av^2\)
2. \(2\rho Av^2\)
3. \(\sqrt2\rho Av^2\)
4. \(\rho v^2\pi R^2\)
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| 1. | \(\dfrac{m}{\rho}\) | 2. | \(\dfrac{2m}{\rho}\) |
| 3. | \(\dfrac{m}{2\rho}\) | 4. | \(\dfrac{3m}{2\rho}\) |
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| 1. | \( P_0V_0\) | 2. | \(2 P_0V_0\) |
| 3. | \({\Large\frac{ P_0V_0}2}\) | 4. | \({\Large\frac{ P_0V_0}4}\) |
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| 1. | \(H\rho g\) | 2. | \(\dfrac{H\rho g}{2}\) |
| 3. | \(2 H\rho g\) | 4. | \(\sqrt 2 H \rho g\) |
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| 1. | \(2R\) | 2. | \(5R\) |
| 3. | \(\dfrac{3R}{4}\) | 4. | \(\dfrac{3R}{2}\) |
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| 1. | \(\dfrac{4S}{r}\) | 2. | \(\dfrac{8S}{3r}\) |
| 3. | \(\dfrac{8S}{r}\) | 4. | \(\dfrac{16S}{3r}\) |
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| 1. | increases. |
| 2. | decreases. |
| 3. | remains unchanged. |
| 4. | increases and then quickly returns to normal. |
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