If we want that minimum three (more than two) ball remain in air then time of flight of first ball must be greater than $4\, sec$.
$T > 4\,sec$
$\frac{{2u}}{g} > 4\;sec \Rightarrow u > 19.6\;m/s$
for $u =19.6$. First ball will just strike the ground(in sky)
Second ball will be at highest point (in sky)
Third ball will be at point of projection or at ground (not in sky)
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A musical instrument is made using four different metal strings, $1,2,3$ and $4$ with mass per unit length $\mu, 2 \mu, 3 \mu$ and $4 \mu$ respectively. The instrument is played by vibrating the strings by varying the free length in between the range $L _0$ and $2 L _0$. It is found that in string-$1$ $(\mu)$ at free length $L _0$ and tension $T _0$ the fundamental mode frequency is $f _0$.
$List-I$ gives the above four strings while $list-II$ lists the magnitude of some quantity.
| $List-I$ | $List-II$ |
| $(I)$ String-1( $\mu$ ) | $(P) 1$ |
| $(II)$ String-2 $(2 \mu)$ | $(Q)$ $1 / 2$ |
| $(III)$ String-3 $(3 \mu)$ | $(R)$ $1 / \sqrt{2}$ |
| $(IV)$ String-4 $(4 \mu)$ | $(S)$ $1 / \sqrt{3}$ |
| $(T)$ $3 / 16$ | |
| $(U)$ $1 / 16$ |
($1$) If the tension in each string is $T _0$, the correct match for the highest fundamental frequency in $f _0$ units will be,
$(1)$ $I \rightarrow P , II \rightarrow R , III \rightarrow S , IV \rightarrow Q$
$(2)$ $I \rightarrow P , II \rightarrow Q , III \rightarrow T , IV \rightarrow S$
$(3)$ $I \rightarrow Q , II \rightarrow S , III \rightarrow R , IV \rightarrow P$
$(4)$ I $\rightarrow Q , II \rightarrow P , III \rightarrow R$, IV $\rightarrow T$
($2$) The length of the string $1,2,3$ and 4 are kept fixed at $L _0, \frac{3 L _0}{2}, \frac{5 L _0}{4}$ and $\frac{7 L _0}{4}$, respectively. Strings $1,2,3$ and 4 are vibrated at their $1^{\text {tt }}, 3^{\text {rd }}, 5^{\text {m }}$ and $14^{\star}$ harmonics, respectively such that all the strings have same frequency. The correct match for the tension in the four strings in the units of $T _0$ will be.
$(1)$ $I \rightarrow P , II \rightarrow Q , III \rightarrow T , IV \rightarrow U$
$(2)$ $I \rightarrow T , II \rightarrow Q , III \rightarrow R$, IV $\rightarrow U$
$(3)$ $I \rightarrow P , II \rightarrow Q , III \rightarrow R , IV \rightarrow T$
$(4)$ I $\rightarrow P , II \rightarrow R , III \rightarrow T , IV \rightarrow U$
