Which of the following symptoms is likely to afflict an astronaut in space? $(a)$ Swollen feet,$(b)$ Swollen face,$(c)$ Headache,$(d)$ Orientational problem.

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(B, C, D) The correct symptoms are $(b)$,$(c)$,and $(d)$.
In the presence of gravity on Earth,the legs support the entire mass of the body while standing. In space,an astronaut experiences weightlessness due to the absence of gravity,so the feet do not swell as they do on Earth.
$A$ swollen face is a common symptom in space due to the redistribution of body fluids caused by weightlessness. As fluids shift towards the upper part of the body,the face appears puffy.
Headaches are frequently reported by astronauts due to mental strain,changes in intracranial pressure,and the stress of adapting to a microgravity environment.
Orientational problems occur because the vestibular system,which relies on gravity to determine orientation,does not function normally in space,leading to spatial disorientation.

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State whether the following statements are true or false:
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$A$ uniform sphere $A$ with radius $R$ exerts a force $F$ on a small particle $B$ situated at a distance $2R$ from the centre of the sphere. $A$ spherical portion of diameter $R$ is cut from the sphere $A$ as shown in the figure. If $F^{\prime}$ is the new gravitational force between the remaining part of the sphere $A$ and the particle $B$,then find the correct relation between $F$ and $F^{\prime}$.

Match List-$I$ with List-$II$:
List-$I$List-$II$
$(A)$ Kinetic energy of planet$(1)$ $-\frac{GMm}{a}$
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$(D)$ Escape energy at the surface of planet for unit mass object$(4)$ $-\frac{GMm}{2a}$

(Where $a=$ radius of planet orbit,$r=$ radius of planet,$M=$ mass of Sun,$m=$ mass of planet)
Choose the correct answer from the options given below:

Match List-$I$ with List-$II$:
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$(b)$ Gravitational potential energy $(ii)$ $[M^{-1}L^{3}T^{-2}]$
$(c)$ Gravitational potential $(iii)$ $[LT^{-2}]$
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Choose the correct answer from the options given below:

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