Write the dimensions of a and b in the relation p = (b-x2)/at, where p is power, x is distance and t is time.

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Step 1: Andika vipimo vya kila kiasi kilichotolewa. Vipimo vya kiasi vilivyotolewa ni: Moment of inertia (I): [I] = [M][L]²; Force (F): [F] = [M][L][T]⁻²; Velocity (v): [v] = [L][T]⁻¹; Work done (W): [W] = [M][L]²[T]⁻² Step 2: Badilisha vipimo hivi kwenye usemi wa x. Usemi wa x umetolewa kama: x = (IFv²)/(W) Badilisha vipimo vya kila kiasi: [x] = (([M][L]²) · ([M][L][T]⁻²) · ([L][T]⁻¹)²)/([M][L]²[T]⁻²) Step 3: Rahisisha vipimo vya x. Kwanza, rahisha kipimo cha v²: [v²] = ([L][T]⁻¹)² = [L]²[T]⁻² Sasa, badilisha na kurahisisha usemi mzima: [x] = ([M][L]² · [M][L][T]⁻² · [L]²[T]⁻²)/([M][L]²[T]⁻²) Unganisha vipimo vya namba (numerator): [x] = ([M]¹⁺¹[L]²⁺¹⁺²[T]⁻²⁻²)/([M][L]²[T]⁻²); [x] = ([M]²[L]⁵[T]⁻⁴)/([M][L]²[T]⁻²) Gawanya vipimo vya namba na denominata (denominator): [x] = [M]²⁻¹[L]⁵⁻²[T]⁻⁴⁻⁽⁻²⁾; [x] = [M]¹[L]³[T]⁻² Step 4: Tambua kiasi cha kimwili kinacholingana na vipimo hivi. Vipimo vilivyopatikana vya x ni [M][L]³[T]⁻². Vipimo hivi vinalingana na vipimo vya bidhaa ya kigezo cha uvutano (G) na mraba wa masi (M²). Kipimo cha kigezo cha uvutano (G) ni [M]⁻¹[L]³[T]⁻². Kipimo cha mraba wa masi (M²) ni [M]². Hivyo, kipimo cha G M² ni: [G M²] = [M]⁻¹[L]³[T]⁻² · [M]² = [M]⁽⁻¹⁺²⁾[L]³[T]⁻² = [M][L]³[T]⁻² Kwa hivyo, kiasi cha kimwili x kina vipimo sawa na bidhaa ya kigezo cha uvutano na mraba wa masi. Kiasi cha kimwili x kina vipimo vya bidhaa ya kigezo cha uvutano na mraba wa masi (G M²). Bidhaa ya kigezo cha uvutano na mraba wa masi (GM²)

Write the dimensions of a and b in the relation p = (b−x2)/at, where p is power, x is distance and t is time.

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Step-by-step solution

Andika vipimo vya kila kiasi kilichotolewa.

Badilisha vipimo hivi kwenye usemi wa $x$ .

Rahisisha vipimo vya $x$ .

Tambua kiasi cha kimwili kinacholingana na vipimo hivi.

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