Question

A shell at rest at the origin explodes into three fragments of masses$1kg$,$2kg$ and $mkg$. The$1kg$and$2kg$ pieces fly off with speeds of $5m{s}^{-1}$ along the $x$-axis and$6m{s}^{-1}$along the $y$-axis respectively. If the$mkg$ piece flies off with a speed of $6.5m{s}^{-1}$, the total mass of the shell must be

• A. $4kg$
• B. $5kg$
• C. $3.5kg$
• D. $4.5kg$
• E. $5.5kg$

Answer 1

The correct option is B

$5kg$

Step 1. Given data:

Shell masses =$1kg$,$2kg$,$kg$,$mkg$

Speeds = $5m{s}^{-1}$,$6m{s}^{-1}$,$6.5m{s}^{-1}$

Step 2. Find$M$ is equal to :

Let the mass of the shell be$M$ which will be the sum of the masses of the fragments$f_1,f_2$ and$f_3$

Mass of

$f_1=1Kg$

$f_2=2kg$

$f_3=mkg$

$M=1+2+m$

$=3+m$

Step 3. Find $m$ :

Linear momentum of the fragments is

$p{f}_1=1x5kg-m/s=5kg-m/s$

$p{f}_2=2x6=12kg-m/s$

$p{f}_3=mx6.5kg-m/s$

Since the fragments$f_1$ and $f_2$flies along the$x$-axis and $y$-axis (at${90}^{\circ }$ to each other)

The vector sum of their linear momentum will be$5i+12j=5^2+{12}^2$

${(6.5)}^{2}m={\left(13\right)}^2$

$m=\frac{13}{6.5}$

$=2Kg.$

Step 4. Find the total mass of the shell :

Total mass = $1+2+2$

=$5kg.$

Hence, option (B) is correct.