MCQ
Zero error of an instrument introduces
- ✓Systematic errors
- BRandom errors
- CBoth
- DNone
Systematic errors in experimental observations usually come from the measuring instruments.
Thus zero error is recognized as the systematic error (factual).
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Assertion $A$ : Body $'P'$ having mass $M$ moving with speed $'u'$ has head-on collision elastically with another body $'Q'$ having mass $'m'$ initially at rest. If $m< < M,$ body $'Q'$ will have a maximum speed equal to $'2u'$ after collision.
Reason $R$ : During elastic collision, the momentum and kinetic energy are both conserved.
In the light of the above statements, choose the most appropriate answer from the options given below:
| column $I$ | column $II$ |
| $(A)$ $U _1( x )=\frac{ U _0}{2}\left[1-\left(\frac{ x }{ a }\right)^2\right]^2$ | $(P)$ The force acting on the particle is zero at $x = a$. |
| $(B)$ $U _2( x )=\frac{ U _0}{2}\left(\frac{ x }{ a }\right)^2$ | $(Q)$ The force acting on the particle is zero at $x=0$. |
| $(C)$ $U _3( x )=\frac{ U _0}{2}\left(\frac{ x }{ a }\right)^2 \exp \left[-\left(\frac{ x }{ a }\right)^2\right]$ | $(R)$ The force acting on the particle is zero at $x =- a$. |
| $(D)$ $U _4( x )=\frac{ U _0}{2}\left[\frac{ x }{ a }-\frac{1}{3}\left(\frac{ x }{ a }\right)^3\right]$ | $(S)$ The particle experiences an attractive force towards $x =0$ in the region $| x |< a$. |
| $(T)$ The particle with total energy $\frac{ U _0}{4}$ can oscillate about the point $x=-a$. |