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Physics-

General

Easy

Question

A weightless string passes through a slit over a pulley. The slit offers frictional force f to the string. The string carries two weights having masses $m subscript 1 end subscript$ and $m subscript 2 end subscript$ where $m subscript 2 end subscript greater than m subscript 1 end subscript.$ then acceleration of the weights is

$\frac{(m_{2} - m_{1}) g - f}{m_{1} + m_{2}}$
$\frac{f - (m_{2} - m_{1}) g}{m_{1} + m_{2}}$
$\frac{(m_{1} - m_{2}) g - f}{(m_{1} - m_{2})}$
$\frac{m_{2} g - f}{(m_{1} + m_{2})}$

The correct answer is: $fraction numerator open parentheses m subscript 2 end subscript minus m subscript 1 end subscript close parentheses g minus f over denominator m subscript 1 end subscript plus m subscript 2 end subscript end fraction$

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Consider the system shown in figure. The wall is smooth, but the surface of blocks A and B in
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Consider the system shown in figure. The wall is smooth, but the surface of blocks A and B in
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Assertion : The locus of the centre of a circle which touches the circles $open vertical bar z minus z subscript 1 end subscript close vertical bar equals a$ and $open vertical bar z minus z subscript 2 end subscript close vertical bar equals b$ externally (z, $z subscript 1 end subscript$ and $z subscript 2 end subscript$ are complex numbers) will be hyperbola
Reason : $open vertical bar z minus z subscript 1 end subscript close vertical bar minus open vertical bar z minus z subscript 2 end subscript close vertical bar less than open vertical bar z subscript 2 end subscript minus z subscript 1 end subscript close vertical bar$
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Reason : $open vertical bar z minus z subscript 1 end subscript close vertical bar minus open vertical bar z minus z subscript 2 end subscript close vertical bar less than open vertical bar z subscript 2 end subscript minus z subscript 1 end subscript close vertical bar$
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parallel

Assertion : Consider an ellipse having its foci at A( $z subscript 1 end subscript$ ) and B( $z subscript 2 end subscript$ ) in the Argand plane. If the eccentricity of the ellipse be 'e' and it is known that origin is an interior point of the ellipse then
$e element of$ $open parentheses negative fraction numerator vertical line z subscript 1 end subscript plus z subscript 2 end subscript vertical line over denominator vertical line z subscript 1 end subscript vertical line plus vertical line z subscript 2 end subscript vertical line end fraction comma fraction numerator vertical line z subscript 1 end subscript plus z subscript 2 end subscript vertical line over denominator vertical line z subscript 1 end subscript vertical line plus vertical line z subscript 2 end subscript vertical line end fraction close parentheses$
Reason : If $Z subscript 0 end subscript$ is the point interior to curve $open vertical bar z minus z subscript 1 end subscript close vertical bar plus open vertical bar z minus z subscript 2 end subscript close vertical bar equals lambda rightwards double arrow open vertical bar z subscript 0 end subscript minus z subscript 1 end subscript close vertical bar plus open vertical bar z subscript 0 end subscript minus z subscript 2 end subscript close vertical bar less than lambda$

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$e element of$ $open parentheses negative fraction numerator vertical line z subscript 1 end subscript plus z subscript 2 end subscript vertical line over denominator vertical line z subscript 1 end subscript vertical line plus vertical line z subscript 2 end subscript vertical line end fraction comma fraction numerator vertical line z subscript 1 end subscript plus z subscript 2 end subscript vertical line over denominator vertical line z subscript 1 end subscript vertical line plus vertical line z subscript 2 end subscript vertical line end fraction close parentheses$
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In the arrangement shown in figure $m subscript A end subscript equals m subscript B end subscript equals 2 k g.$ String is massless and pulley is frictionless. Block B is resting on a smooth horizontal surface, while friction coefficient between blocks A and B is $mu equals 0.5.$ The maximum horizontal force F can be applied so that blocks A does not slip over the blocks B is $open parentheses g equals 10 m divided by s to the power of 2 end exponent close parentheses$

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