An $\alpha$ particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by the above two particles will be:

For the given circuit,calculate the charge on each capacitor in steady state in $\mu C$.

The potential differences that must be applied across the parallel and series combination of $3$ identical capacitors are such that the energy stored in them becomes the same. The ratio of the potential difference in the parallel combination to the series combination is:

In the circuit shown,initially there is no charge on capacitors and keys $S_1$ and $S_2$ are open. The values of the capacitors are $C_1=10 \mu F$,$C_2=30 \mu F$,and $C_3=C_4=80 \mu F$.
Which of the statement$(s)$ is/are correct?
$(1)$ The key $S_1$ is kept closed for a long time such that capacitors are fully charged. Now key $S_2$ is closed. At this time,the instantaneous current across the $30 \Omega$ resistor (between points $P$ and $Q$) will be $0.2 A$.
$(2)$ If key $S_1$ is kept closed for a long time such that capacitors are fully charged,the voltage difference between points $P$ and $Q$ will be $10 V$.
$(3)$ At time $t=0$,the key $S_1$ is closed,the instantaneous current in the closed circuit will be $25 mA$.
$(4)$ If key $S_1$ is kept closed for a long time such that capacitors are fully charged,the voltage across the capacitor $C_1$ will be $4 V$.

The charge on the $4 \mu F$ capacitor in the given circuit is (in $\mu C$)

From a supply of identical capacitors rated $8 \mu F, 250 V$,the minimum number of capacitors required to form a composite $16 \mu F, 1000 V$ capacitor is: