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Physics-

General

Easy

Question

Time period for a magnet is T. If it is divided in four equal parts along its axis and perpendicular to its axis as shown then time period for each part will be

$4 T$
$T / 4$
$T / 2$
$T$

The correct answer is: $T divided by 2$

When magnet of length l is cut into four equal parts. then $m to the power of ´ end exponent equals fraction numerator m over denominator 2 end fraction$ and $l to the power of ´ end exponent equals fraction numerator l over denominator 2 end fraction semicolon therefore M to the power of ´ end exponent equals fraction numerator m over denominator 2 end fraction cross times fraction numerator l over denominator 2 end fraction equals fraction numerator m l over denominator 4 end fraction equals fraction numerator M over denominator 4 end fraction$
New moment of inertia $I to the power of ´ end exponent equals fraction numerator w l to the power of 2 end exponent over denominator 12 end fraction equals fraction numerator fraction numerator w over denominator 4 end fraction. open parentheses fraction numerator 1 over denominator 2 end fraction close parentheses to the power of 2 end exponent over denominator 12 end fraction equals fraction numerator 1 over denominator 16 end fraction. fraction numerator w l to the power of 2 end exponent over denominator 12 end fraction$
Here w is the mass of magnet.
$therefore I to the power of ´ end exponent equals fraction numerator 1 over denominator 16 end fraction I$ ; Time period of each part $T to the power of ´ end exponent equals 2 pi square root of fraction numerator I to the power of ´ end exponent over denominator M to the power of ´ end exponent B subscript H end subscript end fraction end root$
$equals 2 pi square root of fraction numerator I divided by 16 over denominator left parenthesis M divided by 4 right parenthesis B subscript H end subscript end fraction end root equals 2 pi square root of fraction numerator I over denominator 4 M B subscript H end subscript end fraction end root equals fraction numerator T over denominator 2 end fraction$

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If the normal at the points P_i (x_i, y_i), i = 1 to 4 on the hyperbola xy = c² are concurrent at the point Q(h, k), then $fraction numerator open parentheses x subscript 1 end subscript plus x subscript 2 end subscript plus x subscript 3 end subscript plus x subscript 4 end subscript close parentheses open parentheses y subscript 1 end subscript plus y subscript 2 end subscript plus y subscript 3 end subscript plus y subscript 4 end subscript close parentheses over denominator x subscript 1 end subscript x subscript 2 end subscript x subscript 3 end subscript x subscript 4 end subscript end fraction$ is equal to

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Statement 1 : The second degree equation $4 x to the power of 2 end exponent plus 9 y to the power of 2 end exponent minus 24 x plus 36 y minus 72 equals 0$ represents an ellipse Because
Statement 2 : $a x to the power of 2 end exponent plus 2 h x y plus b y to the power of 2 end exponent plus 2 g x plus 2 f y plus c equals 0$ represents an ellipse if $capital delta equals a b c plus 2 f g h minus a f to the power of 2 end exponent minus b g to the power of 2 end exponent minus c h to the power of 2 end exponent not equal to 0$ and $h to the power of 2 end exponent greater than a b$

Statement 1 : The second degree equation $4 x to the power of 2 end exponent plus 9 y to the power of 2 end exponent minus 24 x plus 36 y minus 72 equals 0$ represents an ellipse Because
Statement 2 : $a x to the power of 2 end exponent plus 2 h x y plus b y to the power of 2 end exponent plus 2 g x plus 2 f y plus c equals 0$ represents an ellipse if $capital delta equals a b c plus 2 f g h minus a f to the power of 2 end exponent minus b g to the power of 2 end exponent minus c h to the power of 2 end exponent not equal to 0$ and $h to the power of 2 end exponent greater than a b$

parallel

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